depends on country\company as to if they care about criminal convictions, guess I've been asked about half the job interviews i have done. If you worked freelance it would probably never come up.
web developers are all over the place here at least, some demand for php programmers but only with commercial experience, to many 'graduates' in the market at the moment, every one this it would be cool and easy to work in the web industries.
if i was starting out, i think plumbing (or one of the other building related trades) would be better.