What's the best way to get from London to Shrewsbury in Shropshire County?
What do you want to do when you get there?
Walk around the town for a day or two then head out to Wales. Also, need to know a good clean place to stay in Shrewsbury.
The 'best' way is always subjective.
If you already have a car then I'd just drive, it's pretty easy as it's motorway almost all the way. Try and avoid rush-hour in Birmingham. I wouldn't hire a car specifically unless there was a pressing reason, limited mobility etc.
Otherwise you've got a choice of train or coach (highway-bus in American?). The train's faster but the bus will probably be cheaper.
You can find train times and prices here National Rail.
The main long-distance bus operator in the UK is National Express.
P.S. It's just Shropshire, no need for the "County" - that's what the "shire" bit means.