Hey Ship,
A lot depends on your desired carrier. Starting now, keep an eye on these forums for domicile and hiring info, they were huge in steering my choices (e.g. - staying away from Allegiant). You can start a resume now too. Early this fall, join Airline Apps and take your time building an app for a single airline for free without submitting. When you are ready to pull the trigger next spring, you can pay the fee so as to be able to apply to Delta/United/regional backups at will. You'll need recommendations ready around then too. For SWA/AA/FedEx you can join Global Pilot Credentials and use it to populate apps for those carriers (the rules for counting hours at GPC are a bit different and I don't recall if you can create an app for free there).
Normally, most folks who are jet current can skip a 737 type, esp since SWA doesn't require one anymore. However, keep in mind that UAL at least does sim interviews in a 737. If either is your top choice, the type may be worth it for about $3-4k above what you'd pay for an ATP (it may not be required anymore at SWA, but it is still a plus for getting an interview). I got typed because I'd only flown pistons and drones recently and I wanted to use my GI Bill. Without any heavy experience, getting a type was a huge help at my UAL interview and also made my UAL 737 training almost pleasant. For me, it was money extremely well spent but I am not a typical case.
After getting your ATP, I'd hit submit on your apps by next March (it was four months from submission to starting training for me). You can do your interview prep course soon afterwards while you wait for nibbles from the majors. The regionals will bite immediately, I was 3 for 3 at regional interviews by the time I went to my UAL interview (two months after submission). That experience plus my interview prep made me pretty relaxed for the big one.
I just finished IOE, will be based at my top domicile choice soon, and so far no regrets. Best of luck.