You won't be too old for OTS at the majors. They have hired people in their 60's.
You may have heard that age can be a hiring factor. In the distant past it certainly was, they wouldn't touch you a day after age 30. But the military training obligation was only 5-6 years back then so a 22 y/o college grad could get trained and complete his mil obligation under age 30. That was what they expected you to do and they mostly hired mil pilots.
All different today, mil pilots will be as old as mid-30's before completing their obligation, and it's now illegal to discriminate based on age.
You may have even heard they still do, but it's not really directly age they are considering. Older folks are more likely to have "career stagnation", ie they got suck flying one plane, often an RJ, for 10-15+ years.
Maybe their fault, maybe not. If you get senior at a regional with one type, you are stuck, can't really afford to start over at another regional just to get another type in hopes of *maybe* getting a major interview where you *might* get hired. This happened to many folks after 9/11 when movement got real slow for a long time.
They have two problems with stagnation, they have very compelling statistics the folks who haven't completed a training event in a very long time are a training risk. They will also by definition be older. They also have concerns about a "crusty old RJ CA" adapting to his new role as an FO in a new (to him) corporate culture. There have apparently been problems with this as well.
Older, stagnant, pilots who make the effort to get a new type (ideally at an airline, with some line experience since anyone can buy a type rating with enough money), and also make the effort to attend jobs fairs, network, and interview seem to do much better than their age group peers who just fill out apps and wait for something to happen.
I can attest from personal experience that it's much harder for an older family man to jump through all of the hoops to get and pass a major interview. Much easier when you're young and single (or at least childless). If you do everything right, it's pretty much a full time job and you'll have to keep up the full court press for about a year right now once you're numerically competitive.
So you won't have stagnation issues, even though you started late, you'll be moving along at the same clip as all the kids without any ten years gaps in progress. You will need to be prepared to play the application/interview game hard when the time comes. Start as soon as you meet the mins for the majors, probably about two years into the regional game for most majors (most no longer require any TPIC to apply). Sustained long-term interest is a plus, at the very least apply and keep the apps updated every 1-2 months as soon as you meet mins.
As others have said, unless you have significant background glitches, pick a regional you can stay at comfortably for a long time. If there's one with flow that fits that description, do that since it's a nice backup.