I don't understand why people get their panties in a bunch over "Fortune 500". That doesn't mean they are going to be a good employer. All it means is # 499 can probably afford and justify an airplane...probably...And it doesn't speak what so ever to their reputation as an employer their longevity. Fortune 10, yeah, that's a company that is likely to be around after your dead and gone, but fortune 264? Complete crapshoot. Imagine if there were 500 airlines in the US? How many would be awful to work for?
OP- What type of aircraft, how many overnights per year, how many aircraft, how many pilots? Domestic? International flying?
Always on call is a red flag for me. Although pilots will justify their existence and ego by saying "it's not that bad", it just doesn't have to be that way. Always on call means the department is understaffed.
When you said there is food benefits...Do you know what good benefits are? I'm not being a jerk, I ask because I had no clue what good benefits were at 24. They are a heck of a lot more then good medical and a strong 401K match. Make sure they are offering short and long disability, loss of medical, accidental death, life insurance, FSA for childcare cost, etc...
And in my personal opinion, with a part 121 background and a path to the majors, unless it's a large cabin business jet, I would just stay put. Don't get me wrong, I'm not saying being a part 121 regional FO entitles you or prepares you for large cabin business aviation - it doesn't in the slightest, it's just you have that 121 box checked and could easily be at american or delta by 30. Giving that up to fly a beechjet or citation excel isn't worth it. If you want to push $200k as a pilot in business aviation it isn't a rule, but it will most likely happen when flying a Global, gulfstream or large cabin falcon. Again it's not a rule, but if you can find yourself working for a multi large cabin operator, its the most likely place to also be appropriately staffed, have schedulers and dispatchers, a maintenance department etc.
I know I know I know, all of the above can be found with a citation x operator. As I said, it's not the rule, but if I lost my job I'd be a lot more comfortable with a large cabin type and international experience versus having flying a citation from teterboro to van nuys.
Goodluck!