Muffling of some sort in the bass drum is definitely de-rigeur. It's definitely possible to experiment there though... A couple of pillows or blankets might be considered 'total' muffling; that's a lot of material up against the skin(s) and the resulting sound is going to be as dry as it's gonna get. Varying the amount of 'deadening' material inside, and to what extent it contacts the skin(s) will allow a lot of adjustment. For example, it's quite common to apply muffling that only affects the batter (playing side) head and lets the resonant skin er.. resonate. Obviously all kinds of tuning variations are going to affect the sound here too.
It's worthwhile to try some alternate muffling materials too.. seems folks used to be partial to shredded newspaper in there, but I suspect that the slight noise created by air movement vs. paper would probably show up on the track these days. Thin plastic 'drop sheet' material works well, muffling the skins without absorbing as much sound as a blanket/pillow. The big deal over the last few years has been skins with built in muffling rings, available for both batter and resonant sides. These work really well and have pretty much become standard fare on modern kits, but you'd probably be alright for awhile just messing with different muffling applications for the skin(s) you have beCAUSE... It's a really good idea for you to get bottom skins on those toms. Hopefully you got the hoops and tension rods (tuning bolts) for the bottoms along with the kit... If you do, the easiest way to get those skins is to buy a REMO or EVANS 'head pack', which contains 3 tom heads and a snare head. There are different models available, but you'll be looking for a SINGLE PLY (Remo:Ambassador or Evans G1) set, in either clear or coated. Those are exactly the skins anyone would buy to put on the bottoms of toms anyway (and quite often, on the top too) and you'll end up with a new snare batter head.

Between some judicious kick muffling and a set of bottom skins, you'll end up with a dramatically better sounding kit overall.

Ctrl Z, thanks for the help. I tried a pillow inside the bass drum this afternoon and it sounds much better. Unfortunately, the guy who I bought the set from did not have the hardware for the tom bottoms. Hopefully that isn't too expensive. Thanks.

Hey, I just bought the same kit! I'm not a drummer either.

As far as the kick goes, I'm extremely happy with a sound I got without using any damping material on the head, or in the drum.

Assuming you've removed the heads and then re-seated them properly, if you tune the beater head to give you the tone you want( I went for a low pitched rock concert sounding pop-thump), then tune the front head to a pitch slightly higher. Take the beater out of the pedal, and while lightly striking the beater head with it, listen to the front heads resonance. Keep lightly tapping the beater head and adjusting the pitch of the front head with the key until you get rid of unwanted sympathetic reinforcement of sound waves between the two heads. It worked for me. :D

I also kept comparing the sound of my kick to a live song that I liked the sound of the drums (Hot Tuna-"Water Song" live.

Also do a search for some great tuning threads here on RO.

I'm not a drummer, so don't be afraid to flame me on anything I've said. :c:

You could try a place that buys/sells used gear, Brad... often they'll have old hoops around (put an old hoop on a skin to make sure it's round though!)... The tension rods you'll have to pick up at a drum shop though...bring one off of a top head for length and thread comparison.

Hire in a drum tech or someone who knows about tuning... you'll save yourself a world of pain.