Contract work? How do I even get started?

So I left my previous job (as of this month) and was quickly offered contract work by a past manager who is a higher-up at a different company now. I respect this person, and would be happy to work for him again -- the "unsaid" (on paper) purpose is to bring me in as a full-time employee. That said, I don't even know how to get started with contract work. (I realize that some of this is best answered by a lawyer/accountant, but if any of you could share your personal experiences/opinions, I would appreciate it!)

- How much should I charge, and how do I do it? (hourly, by project, etc) Judging from other threads, I'm guessing that it would be something like (salary/1000*1.3)? This would be for a relatively specific purpose that used to be only part of my old job, and the aim is to charge a rate that would be equivalent to at least $100k/yr, but probably a bit higher to incentive them to just bring me on full time asap.

- Sole proprietorship/LLC: I'll be the only one doing the work, expect that this contract might be the only one, and likely for only ~4-6mos until they bring me on full time. Which business structure is best in this case? I'm assuming this will be 1099 work - do I just end up "paying myself"?

- Are there lawyers and/or accountants who specialize in helping to answer these types of questions, helping small businesses get on their feet?

- Any potential pratfalls I should look out for, or any other general advice?

Thanks all!