I would definitely give the 360 LT M a look. I’ve found it to be incredibly versatile and would work extremely well for any of the styles/artists you’re into. It’s a Jazzmaster-meets-Les Paul Special, after all, so that covers a lot of ground.
Another recommendation as a 290 as your first Collings. It will not be your last! It is a great all-rounder, without breaking the bank. I picked up a nice cherry pre-owned one about 10 years ago. The fit, finish, tuning stability, playability, and tone are all top notch. Since then I've added a 360 LT M, I-35LC, and a City Limits. All keepers. Let us know what you got.