30% to 50% of the price of the instrument is the usual rough rule-of-thumb in my experience, but you'll hear different things from different people. I'd go with carbon fibre unless you would really miss the feel of a wooden stick; you'll get a much better bow for the money. There's an increasingly wide range of choice and quality, and the good ones are a lot more resiliant than wood.

This is one situation where buying new is usually the best option, unless you have a lot of good contacts and a great deal of time (or just luck). Some years ago I bought a mid-range Coda (a 'Conservatory'), and I haven't regretted it. Good balance and not over-light: my playing sounded better, a lot of decorative techniques immediately became easier, and it reduced the overall physical effort required. Something along those lines is all that the average amateur player will ever need.

The original Coda range has been discontinued and I don't know anything about their new lines, but you can find out more at  http://www.codabow.com/models_violin_main.html.

Like a lot of other people, I got mine from Tim Phillips; he keeps a good range in the UK and will give you good advice. He has a separate website for the bow side of the business nowadays (just as well; his range of fiddles is a constant temptation):  http://www.bowshop.co.uk/

Unsurprisingly, there have been other threads here on the same topic, and the general advice given is usually much the same. Have a look, for example, at  Recommended beginner fiddle bows?  which also contains links to other discussions.

Baroque-type bows are growing in popularity, but I'd go with the standard design for the time being. You really need to do all the basic groundwork before starting to explore more specialised options.