As a part-time modular student a couple of years younger than the OP, it's a situation I've thought about quite a bit. Looking from the outside in easyJet seems to be one of the better gigs available, it's a shame they rarely take modular folk.
Staying at easyJet you could probably go on permanent earlies/lates (as a shift worker it's a massive game-changer for the better to stay on the same shift), live 10 minutes from a regional base, be home most nights and when you get a command put loads into the pension due to the lower cost of living at a regional base. IIRC, easyJet have a 2-year secondment option with Virgin Atlantic for a long-haul "try before you buy". From what I understand VS use rotating bid groups for rostering, so the seniority gradient is a bit less steep than BA but there's a theme of VS Airbus crews being worked very hard.
Going to BA, you'll have a strict seniority roster and probably won't get a particularly good roster as a long-haul captain unless there's a mass exodus of more senior folk from the UK. It's not like you'll be able to pick a date 6 months in advance and know if you're going to get it off, especially on long-haul. There's the option of Euroflyer to build seniority before heading to Mainline but you'll take a big pay/cost of living hit in the short-medium term. One thing to bear in mind with long-haul is that you probably won't do much flying, I remember being at an assessment for the old VS MPL programme and an SFO from the airline said that before a trip the captain would ask "does anyone need a landing?" due to the 28-day recency requirement.
If you can get an EASA licence, Aer Lingus might be an option (5:3 short-haul and random roster long-haul) but there is allegedly quite a lot of internal politics which are hard to dodge though very good T&Cs.
For people like us, the dream of course would be for a tweak in the law to require seniority to be done by age rather than join date, much fairer for various reasons in my opinion but that's an entirely different debate.