As with all answers, "it depends". For the US majors, you'll need a 4 year college degree and a lot of quality hours. I know American Airlines is taking pilots from their regionals such as PSA etc, but you'll still need 1500 hours to get a look-in. I have a friend in AA who's played the seniority game to ensure a biddable roster and a reasonable lifestyle. They don't need "command" per se as they'd had a fantastic career in the Air Force and they got all the command time they wanted there.
Many suggest going long haul early, before age and family kicks in. Jet lag is a lot easier to deal with when you're younger. Although at 34 you're starting to get to the back end of the drag curve WRT age and ability to easily cope with disrupted sleep. However, a couple of long haul trips a month versus being worked flat out 800-900 hours a year short haul, well, maybe they can cope a bit better. Needless to say, you need to try it before you discount it - if you have that opportunity.
Living at or near home/in your own country has a lot going for it. Whilst the Middle East and China pay a lot, you're not home, you're a guest in that country and things can go wrong for you pretty quickly if you fall foul of that state's laws and customs. You might love it, but your future partner could very well hate it - assuming you're not planning on being single for the rest of life.
Keep a weather eye on the economy, you might have to lower your sights to "anything with an engine and wings" versus long haul or short haul. If you're lucky, you'll get the job you want, with options to go long or short haul and the company won't collapse just as you sign for that mortgage.
Right now, your job is to do the best you can academically, aim for solid passes and good flight test passes too. Don't stuff up the medical either.
Like any flight plan when you can't get a current forecast for the destination, carry 2 alternates and a lot of fuel!