Your question is pretty general so my answers will be too.
Self defense ammo, anything. Most shooting occure in 6-7ft distances.
Woods carry- a rifle might be a better choice. But we don't have a clue what, when or how you pland to carry in the woods so it is a mute reply anyway.
There aren't a lot of options in 10mm that expand reliably. I would look at Double Tap, Norma, Black Hills and Georgia Arms to see what they have to offer. You want a proven and reliable design. Older rounds like Golden Sabers and Hydra-Shoks are not the best choices. Hydra-Shoks, for example, are well known for plugging and failing to expand when going through clothing. Documentation is all over the internet.
Also stay away from Hornady XTPs. They also have a high failure rate from getting plugged with cloth.
In a 10mm, look for at least 180gr bullet. Anything lighter than that will likely be travelling so fast that it will break up on impact, rather than expanding reliably.
I have to disagree with some of what jonm61 has said.
The 135gr hollow point by Nosler do fragment, consistantly, in 10mm loads, but I haven't seen a single repeatable instance of any of the 155gr or higher bullets fragmenting even in the hottest loads. Also, 180gr bullets have a huge amount of penetration, well more than you need for most SD situations. All of the manufacturers listed, aside from Norma(whom was a pioneer of the FBI 10mm loads, but I don't think even produces their 10mm any more), are more along the lines of assemblers, they don't design or manufacture the bullets used in their rounds so it does nothing to clear up bullet choices.
There are failures in any bullet design because nothing in this world is perfect. ANY hollow point could clog and fail to expand. The XTP is designed to 1.5x expansion, unlike a lot of others, to specifically combat fragmentation. Something designed for intermediate penetration and intermediate expansion is kind of like a politician, the whole point is so that it fits as many uses as possible, which means it's not going to excel at any. I've seen reports of Gold Dots not expanding due to plugging or a lack of velocity. Most of the high expansion rounds like the Ranger T will fold the petals back decreasing actual wound tract unless they hit at exactly the right velocity, which is completely impractical. That's not to say it's a bad round, I love their 9mm rounds, carry them myself.
Get a brand name hollow point in the 150-170 range and it'll get the job done in a SD situation. Get the 135s if you're worried about over-penetration in an urban or suburban environment.
Most of the honest data collected about SD shootings show that a .22LR gets the job done about as often as anything else. If you're bothering with 10mm it should be because of the versatility and maximum terminal ballistics it affords. Why not utilize these traits effectively?
If you don't "roll" your own, Underwood Ammo is another option. The major commercial ammo on the market is more on par with 40 S&W ammo/ballistics. Definitely check out Double Tap, Underwood Ammo and some of the others mentioned for real performance 10MM.