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If one is in the US what bike bits are cheap?
Not cheap, but stuff produced by small volume US manufacturers - King cages, PDW, White Industries costs considerably less if you happen to need it.
Included in that list is Powertap hubs.
Assuming power metres appear in the answers to 1. Should I get one or would it be wasted on me?
If you have some structured training on the cards and £300 burning a hole in your pocket you could do worse than getting a Powertap. But if it came to a toss-up between a PT and a coach / trainer for a couple of months, well, you know...
3a) take own bike, cheaper but hassle or hire one. I probably won't get to ride anything like every day because drinking.