I'm a full-time contractor. One of my clients is based in CA but also has an office in my state. Some random thoughts:

• Dhork's post looks accurate to me regarding state income tax stuff. As a contractor, I haven't done anything at all in CA - I just get paid by my client and count it as normal revenue that I earn where I live. If you go the contract route, I expect it to be similarly simple for you.
• Tax-wise, a person who makes money from work other than employment is by definition a sole proprietor. There is nothing to set up, it's just the word used for that the type of entity that earns contracting income that isn't set up as a corporation or LLC. Even if you made an LLC, unless you elect s corp or c corp status, that LLC is a "disregarded entity" as far as the IRS is concerned and tax treatment would be the same as for a sole proprietor.
• people get worked up about self-employment taxes, but in my case I actually come out ahead because I can dump way more into an individual 401k than I ever could as an employee (employer contribution can be around 18.5% of your profit as a sole prop, on top of the employee deferral). I also run as an s-corp and my state has a PTE tax, both of which let me avoid a bit of federal taxes. But s corp is only relevant if you make like $80k+ from self employment and don't have much other w2 income.
• submitting bids is a function of your relationship with the client and the norms in your industry. I have two clients where I just have an open-ended contracting agreement (both clients had their own standard agreements and I negotiated small changes in one case) and I bill for however many hours i worked every month on projects that are constantly evolving. My standard though is to submit time-and-materials bids for fixed-scope projects. I keep an eye open for fixed-bid opportunities too but I haven't submitted any fixed bids yet.
• contracting is not that big of an administrative hassle so don't let that deter you. But do estimate the tax impact and do either make estimated payments or adjust your withholdings at your w2 job to cover them (this one is easier IMO).
• contractors get a higher hourly rate than employees. Don't undervalue yourself. If you don't have a good benchmark, do some research. I am in engineering services where big companies regularly charge $170-200/hr for my level - I charge a bit below that normally, with a further discount on my long-term open-ended contracts. But the most I've ever made as a w2 was about half that amount, after taking all the tax and benefits stuff into account. I've never fully understood why clients are willing to pay that much, but they are.