I know that the highest catch rate comes from hitting the inner circle when it's smallest, but this is very hard to do, especially when the pokemon is far away.
In cases I know I'll miss, what should I go for? A large inner circle or the smallest possible??
The catch rate is significantly lower if you don't hit the mutli-colored circle at all (outside the white circle), from personal and others' experience.
This question is a bit subjective because it comes down to your own confidence in your PokeBall throwing abilities.
If you are consistent, I would recommend going for the 'Great!' throws, which are harder to hit than the biggest circle, but still boost your catch rate significantly more than the "Nice!" throws.
If you are very confident in your abilities, go for the "Excellent!" throws, but these are the hardest to hit (as you mentioned). Sometimes I like to practice on "trash" Pokemon (low level Pidgeys, etc.), where the stakes are lower, so I can get better at my "Excellent!" throws.
If you are not at all confident in your abilities, stick to the "Nice!" throws, as they are the easiest to hit and reward more xp and catch rate than hitting outside the white circle.
Another note: This is a bit obvious, but the closer the Pokemon, the easier it is to hit the harder throws. My current strategy is I try for "Excellent!" throws when the Pokemon is close up, because with a little practice you can hit these fairly regularly. As the Pokemon backs up (if it escapes), I go for "Great!" and "Nice!" throws, depending on the distance. I also change my strategy based on how many PokeBalls I have. If I only have a few left and I'm trying to catch a more valuable Pokemon, I go for the riskier throws, because I don't want the chance of the Pokemon breaking out and me running out of balls, but this is, again, subjective. If I only have a few left and I'm trying to catch a less valuable Pokemon, I go for the safer throws, because I don't want to miss and waste PokeBalls when the Pokemon escaping isn't as much of an issue.
I also don't try curveballs anymore, as to the extent of my knowledge, the xp bonus does not stack on the xp throw bonuses, but this will likely be fixed in a future update.
EDIT: As noted by @gitsitgo, curveball xp bonuses now stack on throw xp bonuses, as seen here.
There seems to be a misunderstanding of what the inner circle means. From the official Pokemon Go Starter Guide:
You have the greatest chance of capturing the Pokémon while the colored ring is at its smallest diameter. At the opportune moment, fling the Poké Ball toward the Pokémon.
Nothing in there states that you need to hit the actual circle, just the pokemon.
So always try to go for a small circle if you really want to optimise your catch rate. There is no point to waste time to get the best catch rate for a CP10 Pidgey and 200 normal Pokéballs in your backpack. For a rare pokemon with an already low catch rate( inner circle is orange or red) you should make sure that every thrown pokeball has the best catch rate. After a bit of practice you will get a feeling how far you can stretch the timing.
Hitting the green circle is always better than hitting the white outside circle, so if you don't want to waste too many balls, just go for the larger green circle. As you said, it won't give you as high a chance, but it's still better than missing the smaller one.
If you feel that you're pretty good and consistent with your throws, you should probably go for 'great' throws (when the circle is not large but not small either). Otherwise if consistency is a problem, then just stick to the large circle. That's what I do anyway
