Alright, sonic adventure 2 scores are totally different from sonic adventure dx..
I'll try and sum it up for you, but don't expect to be leader just off of this. Basically, rings are much, much, MUCH less sueful than in SADX. Enemies will be your main points.
The basics: on every level (well, almost every) there is a golden beetle. he's worth 1000 points. Killing all other enemies either gives you a 100 or 200 point score boost, depending on the enemy. There is a trick to getting higher scores off of these enemies, though. By killing multiple enemies in succession (either by gliding into them with the gliders, homing attacking with sonic/shadow, or locking on to them with eggman/tails), you get a sort of "trick bonus". for example, if you kill 2 enemies in succession, you get a "good". This good bonus is worth 100 points on your score, in addition to the extras for killing the enemies. If you kill 3 enemies, you get a "nice" worth 200 points. For 4, it's a "great". for 5, it's a "jammin" worth 400. Killing 6 nets you a "cool" for 500. Seven enemies gets a "radical" for 600 points. 8 gets a tights for 800, 9 gets an awesome for 1000, 10 gets an extreme for 1500, and 11+ gets a perfect for 2000 points.
By linking together enemies, your score increases significantly. For example, locking on to 10 enemies will get you 1000 in individual points from the enemies and a 1500 bonus from the "extreme". That's 2500 easy points for your score!
The other things that give points are shields (worth 200 each), rings (worth 10 each, significantly lesser in value than in sadx), time (20 points a second. time bonus is maxed at 1 minute, and you lose 20 points a second after that), and anything else you can get from a capsule, such as extra lives or speed shoes (worth 200 each).
Generally, for all the levels, the idea is to kill as many enemies, get as many shields/extralives, and get as many rings as you can (that aren't out of your way!) in the least amount of time possible. For different types of characters, however, the strategies tend to differ. I'll split it into hunting characters (rouge/knuckles), speed characters (sonic/shadow), and shooting characters (eggman/tails).
Hunting Characters - Alright, the main thing that separates hunting characters from the rest of the characters is the fact that there is no clear, linear path to the goal. Every time you play the level, you have to do a different thing. Because of this, you can't just kill everything in your path and stumble your way onto the goal.
The second main difference is, of course, the emeralds. These emeralds give points to your score and can be the crucial factor in a high or low score. They are a unique mechanic with unique scoring. Basically, if you find the emerald in one minute or less without using hints, you get a perfect 2000 bonus (plus the 200 the emerald itself gives). After one minute is up, it becomes an awesome. After some arbitrary period after that, it drops even more. Using hints also drops the score you get for the emerald. Once you get an emerald, the time limit resets, and you have another minute before yoru new emerald's perfect is expired. Basically, for a top score, you want to get all three emeralds in less than a minute each, using zero hints.
That alone isn't enough, though. Getting three perfects is only 6000 points! You need to kill enemies, collect rings, and get other score boosters on your way to three perfects. And for the highest score, you'll need to do it all in less than a minute!
How can you maximize your scores? There are two things you'll need to do.
a.) you'll need to memorize the locations of easy to get emeralds, and hope these show up in your run.
b.) find the most point-condensed "route" through the level. This route should contain lots of enemies, rings, shields, lives, and all that good stuff that you can kill on your way to finding these emeralds.
Naturally, it will take a lot of time and persistence. But with some luck and effort, you can get some really nice hunting scores!
Speed Characters - Ah, yes. These are my personal favorite characters to score attack as, significantly more so than hunting characters. Anyway, there is, like in hunting, a score mechanic unique to speed characters. This mechanic is known (by me anyway) as "trick points". Basically, on certain levels, for killing enemies in a time limit, grinding rails, doing tricks off of ramps, somersaulting under barriers, or pretty much anything you can think of, you can get "trick points". and easy to check this out yourself is to do a trick off the ramp at the beginning of city escape. You get either a "cool" or "awesome", just like the enemy killing bonus. The difference is just that you did it without killing enemies! These are scattered all throughout the sonic and shadow levels, and are almost essential to a top score.
I know you said you have slow internet, so these links may not be of use to you. I did, however, videotape all the trick points found in certain levels of the game and they could be very helpful to anyone's score. The videos can be found at:
http://www.youtube.com/watch?v=y7m0QRm7uaAhttp://www.youtube.com/watch?v=7oAhitKjeigAnyway, the main goal for score attacking speed character levels is to maximize enemies, rings, capsules, and trick point collection in the least time possible. I would encourage you to check out guides or discover on your own many of the shortcuts and speed tricks in the level, as these will allow you to get significantly higher time bonuses.
Oh, and remember what I said about the enemy bonuses, earlier? Shadow can only link enemies by using either homing attack or light attack (though this is only really useful in one level). Sonic, on the other hand, will maintain combo just by bouncing. If you have homing attacked a combination of enemies together, and you're JUST too far away to homing attack a few more, you can just bounce attack your way over and homing attack from there.
Shooting Characters - Shooting Characters are at the same time both the simplest to score attack and the most difficult to get a high score on. The basic strategy for a mech character score attack is to kill every enemy in sight by locking on to high numbers at a time. Since almost any enemy can be locked on to, and some can be locked on to more than once (hornets), high scores are very easily obtainable.
There are only a few things that need to be said here (well, mostly because it's not my area of expertise).
a.) Your lockon runs out after some amount of time. If you accidentally hold on too long, it can really hamper your time bonus and, subsequently, your score.
b.) locking on to more than 11 enemies is no better than locking on to 11. You get the same 2000 bonus for locking on to 30 as you do for locking on to 11. you may as well get some extra lockons for your buck.
c.) You want to lock on almost every enemy in an area into one lockon (unless it goes over 11). It can sometimes be difficult to stretch out that awesome into a perfect, but it's worth it for your score.
Well, I attempted to make a detailed post for you. I'm not sure it's as long at I expected it to be (it actually seems like I know much less than I do). Regardless, I hope there's enough info in here for you to get some very good sa2 score attacks. I didn't directly answer your question, so I guess I will now: Time is more important than rings, but don't be afraid to get 10/20 capsules.
Anyway, hope this helps. If not you, maybe it will help someone else.