Each bow is rated for how much force is needed to pull the string back to a specific point — i.e., "40 lbs @ 28 inches" means it takes 40 pounds of force to pull the string back 28 inches. As long as your aim is spot-on every time you send an arrow towards the target, it doesn’t matter how "powerful" the bow is. **For all those who say that a "kid’s bow" doesn’t have enough power to send an arrow more than 10 yards — I have personally witnessed a 40-year archery veteran using a 60 pound-draw compound bow lose out to a 15-year-old using a 20 pound-draw fibre-glass longbow — at 30 yards; yes, the kid really was that damn good, and he really was using a REAL BOW. I’ve seen a 20 lb bow send arrows more than 80 yards, and with a fair amount of accuarcy, considering.

Now, before you go out and buy yourself a bow, you need to check with your local authorities as to whether it is legal to practice archery in your yard/garden (go to the County courthouse/City Hall/Mayor’s Office/etc – don’t ask only the police, because they don’t like to do the paperwork and they might just say "no" regardless). If you live in a city, it will most likely NOT be legal.

IF it is legal for you to practice archery in your yard/garden, I suggest that you start with a low-poundage bow, around 20 lb draw; regardless what others might say it is much easier to learn on a light-weight bow than on a heavy-weight bow — simply because the light-weight bow is easier to control (if you can’t control the bow, you won’t gain any real skill as an archer). As you gain strength and skill, you can increase draw weight (easy to do with a compound, but you will have to get another bow if you decide to get a "traditional" bow – a bow without "wheels").

Beware of using only hay bales or straw targets — arrows have a nasty habit of passing clean through them due to "soft spots" in the bales. You need to have a good backstop BEHIND the bales/target; the target is attached to the "front" of the bale(s). A good backstop can be made by hanging discarded carpeting between the bale(s) and the fence; do not attach the backstop to the fence, or it will never keep the arrows from hitting the fence; tightly woven carpeting has been known to stop even broadheads. (Don’t hang it tight, hang it loosely; the carpeting will "catch" the arrow, absorbing the impact, and allow it to simply drop to the ground). Wooden fences generally do not make good backstops, by the way, because the arrow can break when it hits the fence; metal fences NEVER make good backstops, for what should be a very obvious reason.

Targets can be made out of cardboard boxes, stuffed with more cardboard or plastic bags; pre-made styrofoam cubes sold in archery shops; burlap bags stuffed with plastic bags and/or paper bags; paper plates; a piece of cloth; etc. If it can be placed in front of or attached to the target butt (the hay bales), and it won’t damage your arrows as they enter/pass through it, it can be used as a target. If you keep the target(s) low to the ground, you won’t have to worry too much about arrows going too high — but sometimes arrows will "skip" when they hit the ground, too, so be careful; about stomach height is good for placing the target(s).

Now, for those who say that a huge amount of space is required for archery (no matter how "powerful" the bow is), it is more than merely possible to practice indoors at home — say, in an apartment; just hang a tight-woven blanket in a doorway (fasten it down ONLY at the top, leave the sides/bottom loose – just like with the carpeting backstop above) and use blunt-tipped arrows (rubber blunts work really good for this). You shoot at the blanket, the blanket "catches" the arrows — and the arrows drop to the floor. Yes, it really does work……

In all cases, make sure it is SAFE to practice archery. Be sure of what is behind the target/butt at all times; one of the worst experiences in life is to kill someone — perhaps a child — because you didn’t bother to make sure it was safe to shoot. If you use the blanket-in-the-doorway method, use a doorway that you KNOW will not be used while you are practicing — and when in doubt, ***block the path to the doorway*** on the other side of the blanket. SAFETY — FOR YOURSELF AND OTHERS — SHOULD ALWAYS COME FIRST IN ARCHERY.

Make sure it is legal to practice archery in your yard/garden first, and if it is — have fun.
References :
30+ years archery experience; doing, learning, teaching, researching — not always in that order. I have my own 30-yard outdoor practice range at home, down the hill from the house and just off the drive.

Generally speaking….and this is a rough estimate….you can figure on an arrow traveling 10 yards per pound. That’s if you were shooting upwards at an angle with the intent of max range. A 30# bow would reach out to 300+ yards. Ebay fiberglass Bear bow with off the shelf arrows, you can cut that in half, though.

Lighter than 30# and you’ll be in the neighborhood of kid’s bows and learning to shoot on one of those is actually quite a bit harder than a real bow. It’s easier to learn on a consistent middle weight than a poor light weight.

Addendum: **For all those who say that a "kid’s bow" doesn’t have enough power to send an arrow more than 10 yards**

If that’s what you got out of that post, bud, perhaps you need a refresher course in reading comp? I said you won’t find any kids’ bows on the common market that are consistent at those lighter weights, not that they couldn’t shoot that far. The lighter your bow weight, the more your arrows’ weight comes into play….and anything less than 30# or so won’t shoot consistently enough to learn the sport. One arrow might fly straight and the next drop to the ground half way. The power of a kids’ bow has nothing to do with anything….the consistency and the ability to throws arrows at a constant velocity are all that matters.
References :

Oh, did you mean how far they can shoot? Different for every bow.
References :

Go to an ARCHERY SHOP, not Cabela’s, Gander Mountain, Wal-Mart, Holiday Sports, Scheel’s, or even Sportsman’s Warehouse — in fact, just forget the "Big Box" stores altogether; they want to sell you what "looks good" or is "popular", not necessarily what you actually need. At an ARCHERY SHOP, you will find people who are experienced in archery/bowhunting and know what is needed for "____" (as opposed to the folks at places like Cabela’s, where – if you are lucky – they MIGHT have some real experience in their ‘department’ (most of the time they work 2 or 3 ‘departments’, so how can you be sure they know what they are talking about?); I walked in to a Sportsman’s Warehouse last year and asked how much actual archery experience the sales-guy had, and was told "Oh, I’ve been shooting bow and arrow for two years now". NOT a good sign, and Wal-Mart is ten times worse; don’t go there unless you already know what you need).

The bow has to fit your hand, it has to feel right in your hand, it has to be the correct physical weight in your hand — and YOU are the person who will be using it, not the one that sells it to you. If YOU don’t like it for whatever reason, it won’t be anything other than just an expensive piece of junk because your experiences with it will always be less-than-perfect (even on those rare occasions when everything "clicks"). "Power" is often over-rated, since even a 46 lb-draw longbow can be used effectively to kill large game — including bear.

When you try out the bows at the archery shop, don’t stop with compounds — try some of the recurves and longbows, too (if there are any). You won’t know if you like them until you try them.

And then there are the arrows. The "perfect" arrow for one set-up most likely will not work at all for another set-up. They MUST be matched to the bow/archer/intended use combination for full effectiveness. Get the wrong arrows, and that "perfect" bow can become the worst investment ever. And "quality" does not always equal "expensive"….ten years ago I paid a "professional" fletcher $60 for a dozen arrows — and they were junk; I now pay less than $40/dozen (total cost for shafting/fletching/points/nocks/etc; sometimes you can get a discount on supplies by "doing favors") and build my own, and they are nearly perfect. Get the best that you can afford, at the very least.

Hope it helps, if only in some small way.
References :
30+ years archery experience; learning, doing, researching, teaching — not always in that order.

If this is the case then an air rifle with a 1000+ feet per second speed would be a good option and easier to use. Other than that, any bow with a light pull weight would suffice, anything around 30-40 lb draw.
References :

The furthest distance shot with any bow is 2,047 yards (1,871.84m) . This was shot by the late Harry Drake in 1988 using a crossbow. The furthest with a hand-held – and pulled – bow is 1,336 yds 1′ 3" (1,222.01m) , shot by Don Brown with an unlimited conventional Flight bow in 1987.

Target archery and flight archery are very different. Target archery is scored for accuracy at standard distances. Flight archery is scored only for distance where the arrow lands on the ground. Bows are different, arrows are different, techniques are different. There is really no comparison.
References :
http://en.wikipedia.org/wiki/Target_archery
http://www.second-opinions.co.uk/flight.html