Hi, I'm not the world's biggest expert, but the things I look for are:
1) Free is good. It's even better if someone else has already cut it down!
2) STRAIGHT GRAIN. The bark will usually clue you in. The straighter the better if you're just starting. Twisted logs are a real pain to split and sure you can steam out some propeller, but it's a lot of work. Wavy logs produce wavy staves, which is OK if you like character staves, but you will have trouble tillering character staves.
3) Given a choice thinner rings = stronger wood for most conifers (yew, junipers, etc.) Thicker rings = stronger wood for most hard woods, especially ring porous woods like oak or elm. Trees growing in the open with plenty of water have the widest rings. So, look hfor ardwoods growing in good conditions, but look for conifers that have been growing under harsh conditions (ie. high elevation, high latitude, deep shade.)
4) Avoid dead trees unless you're really sure the wood is still sound.
5) Trees are heavy! Logs over ~ 8 inches in diameter quickly get difficult to handle, and potentially more dangerous to fell. I like 4-6 inch trees, cause they're easy and safe for one person to handle. You can get a lot of staves from one large tree, but you had better have husky friends, power equipment and experience felling trees.
Ron