Well what are you looking to do with your car? Do you plan on taking it to the 1/4 mile track, auto-cross, just cruise around in? You thread title gives the impression you are just asking about exhaust. But your post makes it seem like you are curious about your first mods??
But yes, I would definitley do exhaust. Cat-back for sure. And get a aftermarket mid-pipe if you want more sound and a little bit more power. Maybe headers as well.
Steeda Springs and CC plates
PRo 5.0
Bilstein shocks/struts
KB front and rear strut bars
KB subframes
Catback + offroad pipe
Steeda MIL eleminators
K&N intake
Bassaini midlength headers
I am sure there is stuff I forgot but thats my list so far of wanted stuff.
Gears, gears, and gears...but yeah, what do you intend to do with the car?
There are several proven bolt-ons out there:
Gears, shifter, catback, X or H pipe, underdrive pullies, timing adjuster, cold-air-intake/new air filter & MAF...then you get into the more involved stuff like headers ($$$ for install), custom tuned chip, suspension mods and whatnot.
The mod that got me the biggest rush where the gears by far.
If you want your Cobra to sound mean (which was imporant to me as well) then go with a cat-back exhaust. If you want it to sound really mean get an off-road H pipe as well. Long tubes are a great mod, but it doesn't really do much to the sound exept make it deeper....but it does give you some good low and mid range power over the stock manifolds.
A Tri-ax or Pro5.0 shifter is a great mod...not expensive, feels better, and adds safety to the transmission.
Lowering it makes the car look good...but do it right the first time. Get the springs, shocks, struts, and CC plates. I did this in stages and I wasn't happy until it was all done.
Since you are just starting to mod, I would say go with the exhaust mods and shifter...once the bug takes over, you will figure out the rest just like we did.
I'd go with 4.30 or 3.73 gears if you ever plan on doing the 1/4 mile. 4.10's and the redline of the 01 Cobra will be too much for third gear and not enough for fourth gear. 3.73's are just right to finish the 1/4 in third gear N/A and fourth gear with a power adder. Just my opinion though from what I have witnessed from fellow Cobra owners here in town.