Someone once said "speed is the by-product of accuracy"
Yes I agree, good point, take a peace like Flight of The Bumbelbee, transcribed by Troy Stetina. Start with something slow like 75bpm. When you have it down and can play it cleanly then increase to 80bpm and so on, start slowly and before you know it your at 100bpm.
If you don't want to play super fast then pick songs that you want to learn, go over the fast part, analyse what scale he's playing, play that scale with a metronome at a speed that's comfortable to you and that sounds clean, then increase the speed gradually.
Use a clean sound when you practise technique, distortion can mask or hide some flaws in your techinque.
Write down everything you do, like Bumbelbee 25 minutes, 75bpm.
Then you can go back after 3-4 weeks and see, hey I'm at 85bpm now.
It's fun an rewarding and actually shows you how much you actually practise.
I set a weekly goal, like this week I want to hit 20hours, that's hard for me
with 8-5 work and three kids but you set your priorities in life, I don't watch that
much tv or play video games, instead I play guitar and see progress.
You said you don't want to become Paul Gilbert fast but his videos, mostly Intense Rock, Vol. 1 and 2 and Terrifying Guitar Trip are awesome for getting faster.
And hey he's funny and entertaining and for me keeps guitar fun and exciting, I have played them for some time now and I'm not anywhere near Paul Gilbert fast
The stuff from our fellow Jemsiter JackButlerGOT is good stuff, IntelliShred and Arpeggio Madness check that out.
Like the others have said, start slow and cleanly but remember to increase the speed, don't get stuck at medium speeds, always push the envelope.