I am currently using an ADSL internet connection running at 3008kbps/512kbps max and I would like to know what should I choose in the speed section in Limewire options.

cable/dsl should be fine, or T1 if you feel like you want to download and upload faster. (always remember to share!)

if you dont have a T3, do NOT use this option, it WILL max out your connection and make it appear really slow on other applications.

But which option is the best though?

personally, i have about the same download speed as you do, so i set mine as a T1.

a t1 = 1.5Mb/s
mine is 3Mb/s and yours is really close to that. so its double a T1, so the T1 setting should work perfectly fine.
however, my upload speed is 768Kb/s which is equal to 0.75MB/s... yours is 0.50MB/s

yea i think setting it as a t1 should be just fine. it would maximise your upload/download bandwidth to its full potential. (you will see more sources being swarmed from.)

Thank you for the help and are you having the problem that I have: I don't know why, but everytime I load this page I don't see some Icon and they are replace with red x. If you do, do you know how to fix it?