Paleo Planet is the place for more information than you could possibly absorb.
Harvesting your own timber is great, but I always suggest newcomers use shop bought Ash or Red Oak (or similar) to practice on than risk harvesting a bunch of staves only to turn them into matchwood.
Saplings or boughs of a couple of inches in diameter are more than enough to make a hunting weight bow - you can rough the bow out from the green wood and leave it slightly oversized, coat the ends with glue to prevent splitting and season them for a month or so in a warm room in the house and they should be good to use. Larger timber obviously requires more time but by removing the excess you remove the amount of material you are trying to season plus it's easier to take off when it's green.
Hazel and Ash coppice is a great source of bowstaves...
Easiest, safest and most reliable bows to make are pyramid bows - wide limbs immediately above and below the grips sharply tapering to fine tips. Pyramid bows can be fast shooting and an advantage of that much material in the width of the limb means the limbs need not be as long as on a narrower design.
Moisture content and tillering are the two areas you need to concentrate on but only
AFTER you start to understand bow design in relation to particular wood species.
Basic rules of thumb:
If in doubt, make the bow wider.
Narrower bows
can shoot faster but they can also de-stabilise if you aren't very careful. Particularly dense tropical hardwood like Ipe are wonderful - most of my Ipe longbows are a shade under an inch wide. It is so dense that you need less of it to achieve the same result as with other timbers. Most folks make their first Ipe bow the same dimensions as they would use for Yew or Osage and then wonder why they can't even string it, never mind draw the thing...
Make straight bows at first because if you can't tiller one of them then a reflex or combined reflex/deflex design will have you a gibbering wreck.
Don't waste time with sinew or similar backings unless you can successfully make bows to begin with - backing a bow, even with rawhide, takes time and effort to do properly and there is no sense investing that if you aren't pretty sure of the likely outcome.
You can make bows from loads of British timber, ranging from Dogwood, Hawthorn, Walnut, Lime, Ash, Wych Elm (one of my favourites), Sycamore, Laburnum (my number one favourite), Yew (obviously), Hickory, Hazel, Juniper and so on.
Concentrate on a straight pyramid bow and then move onto a longer and narrower more stacked design like a longbow.
Once you have your tillering nailed feel free to play all you like with backed or reflex/deflex design.
Anything up to around 40lb or so draw weight and you can afford a little grain wander, but straight grain is always better to have if you can find it or, at the very least, allow your bow to follow the grain if it drifts, ending up with a wobbly 'character' bow.
Lots of fun, bow-making, and all you need is the right timber, a saw, Nicholson rasp and a couple of scrapers (knife blades will do).
A few of mine:
One of my laminated longbows, overbraced, drawn and just unbraced:
The slight set recovers after half an hour or so, almost to dead straight
Bamboo backed Osage, 92lb @ 31" shown braced, at 20", at 30" and the at rest immediately after unbracing, with barely an inch of set:
Longbows have been a lifelong passion of mine, probably even more than knives and knifemaking, and I am always questing after an ultra-fast and smooth shooting longbow that has as close to zero set (string follow) as possible.
Happy to help if you come unstuck either in the forum, by PM, email or phone.