Sounds like maybe you need some terminology to start with:
A "trigger" is a device which senses impact and converts it to an electrical pulse. There will be one or more trigger in each electronic drum.
A "module" is a device which converts the impulses from the triggers either into a drum sound, a midi message or both.
Modules will have several input jacks in them to run a cable in from each trigger, and usually have a way to adjust for things like input sensitivity, etc. They will also allow you to assign the various built in sounds to each channel.
Popular sets such as the Roland v-drums have modules which have some pretty good built in sounds from my understanding, but the price tag on the whole set-up is going to be higher than your budget.
I am in the middle of these issues myself. I'm a guitarist and recording hobbyist who wants to try edrums for tracking (tired of trying to program drum tracks in my sequencer). Like you, I don't want to spend a lot of money, I just want something that works. I do have some pretty good drum samples in my pc (I have Gigasampler) so I really don't need an expensive module with built in sounds. So here's what I'm trying to do - maybe this would work for you:
First off, I just purchased a used Roland PM-16 ($100 on ebay, it arrived today

). This is an older unit which is now out of production, but should work fine for my purposes as opposed to the new modules which start at $400 and go up from there. It has no built in sounds, but what it does have is inputs for up to 16 triggers as well as midi in and out. Each trigger input can be assigned to transmit a different midi note. This will be connected to my pc via my usb midi interface. I will load up a kit in my gigasampler to play the sounds based upon the midi messages coming from the PM16.
For "drums", I'm going the do-it-yourself route, using Remo practice pads which I will modify with cheap Piezos (triggers) and a few other miscellaneous inexpensive items. The pads cost between 12 and 18 dollars each from Musicians Friend and with the additional parts should run between about 25 to 30 dollars per drum. There are instructions on the web for making these, do a google search, or go to
www.electronicdrums.com. I plan to make a rack to mount these on using ABS pipe and PVC fittings. I'm working on a scheme to mount the drums using inexpensive hardware available at Home Depot.
When all is said and done I expect to have full e-drum capability for much less than your budgeted amount of $600. The only other option I've seen in this price range is the Ion set which runs about $300, but in my opinion that looks like a pretty flimsy setup. My set will be much more sturdy and have a lot more drums for not a lot more money - it's just gonna take a little work.
Well, hopefully that clears a couple things up for you and gives you some ideas. I've rambled enough for one post, but if you have more questions or you're interested in hearing more about my edrum project, let me know and I'll ramble some more
