I was worried about this same problem. i had a small 10 watt Marshall Mg that I played with a les paul. It was good for quiet practice in my basement but i wanted bigger sound. However i didn't have big money to go spend on a tube amp or anything. What i did have was a Fender Acoustasonic 30watt amp. Even with an electric guitar plugged in it have a great clean sound and a nice array of digital effects.
After doing some research I bought the fulltone OCD overdrive/distortion. and surprisingly it sounded awesome once i plugged it in to the acoustasonic amp. Plaing around with it i got sounds ranging from john mayer blues tones to slash and even some heavier metal tones.
the most important thing is to realize that all amps are different and react differently to different pedals and effects. In my case i turn the treble on the amp all the way down because the pedal provides tones and also keep the bass on the amp down because the pedal boosts that too.
So long as your amp has a 3 band eq (bass, middle, and treble controls) and the drive/distortion pedal has good tone adjustment on it you can dial in the tone with any amp/pedal combo.
So to highlight points, it doesn't matter if your amp is tube or solid state, every amp sounds different with every other pedal, and the more tone adjustment you have the easier it is to get the tone your looking for. Oh yeah and the Fulltone OCD is a killer pedal.
Basically the only way to know how its gonna sound with your amp is to buy it and try it if you dont like it be clear on the return policy. but your amp wont explode.