Not sure what to recommend. I've read a number of times Jerry used Fender Twin Reverb amps, so some kind of effects device(s) was used. Try doing a web search and see what you come up with. A multi-effects pedal may help you pinpoint the sound(s) you're looking for. In the meantime, since you're such a Dead fan ( great to know some of you youngsters are into the Dead ), check this website for many Dead tabs.

http://www.rukind.com/