Excellent questions. I will endeavor to answer:
I started playing for a few hours. After getting to a whopping level 3 (mostly just pickpocketing and sneaking around the starter town) I'm not sure I get the perk and leveling system.
In Oblivion, the "perks' unlocked automatically when your skill level reached the required level. So you got x6 backstab for free. In Skyrim, you can be really sneaky (hard to detect) and never spend the perk on backstab, and thus NOT get x6 damage.
So, if I raise a skill up, does the skill actually improve in any way, or does it just allow me to meet the prereqs for perks that improve the skill? Does a guy with 90 One-Handed Weapon skill attack more effectively than a guy with 20 if neither invested in the appropriate perks? Does 90 Sneak evade detection better than 20 Sneak without perks?
Spending points on skills, improves your chance of success. The perks usually don't impact the skill, but the skill level is required for the perk.
Sans perks, a guy with 90 on a skill is better than a guy with 20 on the same skill. It's kind of like there's a die-roll for each attempt to use the skill.
Case in point, Sneak. Sneak gives you skill/2 = % as your chance of detection (per time the computer checks). So, with 100 sneak being max, the best you can get with skills is 50%
Also, I see that the perks can be taken multiple times. For instance, One-Handed has a perk that increases one-handed weapon damage by 20%, and it can apparently be taken five times. Now, do I get a 20% bonus every time I take the perk (ramping all the way up to +100%)), or does the perk not unlock at all until I take all five ranks?
Continuing the example about Sneak, there's a Perk you can take 5 times to improve your sneak %. The first time improves it with 20%, the next time improves it to 25%. I don't know what the next bumps do, but if you had maxed your sneak points to 100, you'd have 50%. Buying the perk twice would add another 25% to get you 75%.
I suspect they did the math such that it is VERY hard to get 100% hidden, so as to avoid the invisibility problem Oblivion had (I could get 100% chameleon, and I had maxed Sneak, NPCs could be angry at me and never see me to attack).
Anyway, how is archery working out? I never got anywhere with it in Oblivion because it was so slow that it was only good for a single shot against an unaware target.
In Oblivion, higher levels of Archery would let you Zoom in (left trigger) while you've got an arrow drawn (right trigger). It was like running a sniper in Call of Duty.
I'm not certain of the other perks in the Archery chain.
I highly recommend the
Unofficial Elder Scrolls Wiki for looking this stuff up.
If you plan on picking locks, the Lockpicking tree has perks to make Novice, Apprentice, etc level locks easier. This seems to mean that the vibrate lightly when you are about to break them, rather than vibrate hard and break easily.
For spells, the first perk makes novice spells use less magicka(the default spells you have being novice destruction and healing spells). It's a good buy if you cast any spells during combat (heal hand, sword hand strategy would be nice to use less mana while fighting)