Yes the latest sample that I put up had some compression, however I didn't use any limiting.  I basically followed the cakeTV video, how to get bigger drums, to start with and the tweaked from there.  

I'm in agreement with Danny.  You don't have to have a "perfect" sounding kit for it to sound good in a song.  I didn't think there was anything wrong with the snare ring.  In the right song a ringing snare can sound pretty cool.  Take for example:
http://www.youtube.com/watch?v=ARiiO_41Id8

I think it's more important that through experimentation, you learn what it takes to get various sounds.  Then depending on what the song needs, you'll know how to get it.

Hi Olive-

First, I have to say that Danny's comments are great, and he is one of the most altruistic people that I have (never) met. 

The first thing that jumps out to me is to ask the question: "What type of material will you generally be recording?"

The reason I ask, is that I think your kit sounds pretty good. I agree with comments about the timid playing and such, but the toms sound like toms and not boxes. The snare sounds like a snare. Sure, I may tune it differently for my type of sound, but I did not think that it was over ringy at all. 

So, from a guy who has spent years trying to dial in drum sounds, I think you are off to a great start. I think that it would be helpful for us to hear the kit and the drummer in the song. Maybe some tracks of the entire song and then just the drums. But, I repeat that I think that your capturing of the natural sound is good to start. Depending on the performance, you may have little work to make this kit sound great in a mix.

I hope you post more.

Echoing others saying you need to punish those drums a little more :D

You won't get the tone and character out of a drum unless you hit it hard enough to get the shells to resonate, otherwise you are just hearing the skin ring.

Going on 30 years drumming with students often a little leery of laying into the things, that's what I hear, the timid sound has nothing to do with compression, and it's not just me being a hard rock/metal drummer, drums really need to be hit with a certain force to get them to open up no matter what style.

Try another recording, this time hit them hard and you'll hear the sound open up and get the character of the kit out.

Also, you can get rid off a lot of snare seiding resonance by experimenting with tuning your toms if you have problems with sympathetic resonance, much better than killing the snare with muffling. Get a tune-bot and experiment with tuning.