Pedals can't do for you what a good tube amp can.

But you might want to look into some overdrive pedals. Like an Ibanez TS-9 or TS-808. Just beware of their marketing tactic. They want you to think SRV would only use a TS-808 when in reality he also used a TS-9 (which is $100 cheaper). You should also look into a Boss Blues Driver, which has a bit more gain. I've played through one and I liked it a lot. If you have a slightly larger budget look into a Fulltone OCD or a Fulltone Fulldrive 2. If you want something versatile enough to handle everything from pop to punk to rock to blues then look into a Visual Sound Jekyll and Hyde.

I always play though a Screamin' Eagle that was custom made from http://www.sbnpedals.com/. It has three different overdrives in one, plus bass boost. It's the best sounding overdrive I've ever heard and it's the best bang for the buck.