No one would confuse the sound of the Beatles with the sound of the Def Leopard, nor would one confuse the tone of SRV with the tone of BB King. Both rock and blues, respectively.
It also depends on what amp you have, what pedals you might own or care to own. It really comes down to experimentation. For blues, start clean and add overdrive to taste. Try scooping out the mid range (lowering it compared to base and trouble), this creates some extra separation between the high and low range. Have fun, take notes of the settings you like.
What you might want to look into is a small processor like a Line 6 Pod or a Korg Pandora. Each have tons of preset tones and amp models to play with.
http://line6.com/podxt/ Line 6 Pod XT
http://www.korg.com/Product.aspx?pd=290 Korg Pandora PX5D
I have the Korg PX4, purchased it the day after I saw someone else with it about 6 years ago. If you're a good EBay'er you can probably get a good deal on some older stuff.
Best of luck with it.