Way too often, people forget the importance of the instrument itself -- or the amp it may/may not be plugged in to. Put your money in to a better kit or a better guitar, and it will do a lot more for you, 9 times out of 10, than a better drum mic or processor, etc.
All other things being equal, everyone will have a much different theory on this, so it's going to depend a lot on who you ask. It also depends a lot on your personal priorities and tastes, and what kind of music you do.
With that in mind, I've put together a few theories here for you, because I'm bored and feel like ranting. Which one of these is right for you depends on your unique situation. And most of all, what your long-term goals are versus your short-term :
1. Weakest Link Theory:
Ask yourself if it is important to you to get an immediate improvement via instant gratification, or if it is your goal to slowly make baby steps toward an improved gear list.
If your answer is "instant gratification," then the
Weakest Link theory is what you should follow. The best place to start should be at your weakest link. Determining what your weakest link is might be a little tricky, but after playing around with something for a while and asking enough questions, you should be able to figure it out. If you can't, for the life of you, figure out, then chances are you need to brush up on your skills before you buy anything. By the time your skills reach a certain level, you'll know what's holding you back.
The idea behind the weakest link theory, of course, is
addition through subtraction, and provided it's a big enough upgrade, you should hear immediate results.
II. Reverse Signal-chain theory:
The reverse signal-chain theory is based on the idea that "I am mostly happy all of the gear I have. There are no glaring weaknesses that I can think of. I just want to start upgrading, but I'm not sure where to start."
If this sounds like you, then this is your game plan. The idea behind
reverse signal chain is to start with the source and work your way along the path (journey) the signal takes, following each successive step untill it ultimately makes it's way to tape or disk.
Start with
the performer, then
what the performer is playing, then
the room he/she is playing it in, followed by
the microphone capturing it . . . working your way down to
what the mic is plugged in to eventually making your way down to
the medium it's recorded to, which would include A/D conversion, clocking, etc.
Amendment I: Weakest Link Amendment
Again, the weakest link clause has to apply as an exception to the reverse-signal chain rule. For instance: start with the player and the instrument
unless you have a much weaker link on down the chain. If that's the case, take care of that, then go back to the source and work your way back.
The logic being that it doesn't matter how good your A/D is if the mic sucks . . . and similarly it doesn't matter how good the mic is if the weakest link in your chain is a Soundblaster card recording at 8 bit

, or if there's an Alesis compressor molesting your signal on the way to the soundblaster, etc. etc.
Amendment II: Bargain-hunter's Clause
The idea behind the bargain-hunter's clause is very simple. Select your plan, be it the weakest-link plan or the reverse-signal chain plan. Stick firmly to your plan
except in cases where something comes along at an unusually good price. Examples of this would be if you're saving up for a new mic pre, when suddently you see an ebay auction about to close for a used Apogee Rosetta converter for like $200.
In that most unusual of circumstances, you'll want to check the seller's feedback rating, ask him a few questions, and if you feel good about the opportunity, then move on up the chain for the time-being and get that convertor. Just make sure to move back down to the mic pre the next chance you get.