Corporate finance out of undergrad or as lateral hire?

Most corp strat/corp dev jobs are lateral hires from consulting and IBD. So, if that's what you want, that's the way you should go. Corporate/commercial banking and valuation might make corp dev a possibility, but less so. Big 4 laterals tend to go into more traditional CF roles like FP&A.

I'd say, depending on the company, the FLDP is similar in helping you achieve a corp dev/corp strat role. Though, some companies don't even really get FLDPs into those roles and almost completely staff laterals. As far as non-rotation CF jobs, they are usually pretty tough. Much harder to move up than the other lateral jobs or FLDPs. Generally much lower paying than FLDPs or the other jobs you are talking about. But you can still make it work if you perform at a great level and get people to believe in you. Again, it will be hard to get into corp dev/corp strat, though.

As far as your pay concern, large companies and entry hire programs generally have set salaries they give new undergrads and there isn't much wiggle room. Boutiques and smaller firms are easier to negotiate with. But large companies and entry training programs generally don't allow that until you are farther into your career.

My suggestion, from what you sound like you like and want to do, get a consulting gig. Then lateral into corp strategy later in life. That's the easiest path for you.