It depends on the mission, but most have the player's airbase pretty close to the action - anything more than about a 10-15 minute flight to the target is unusual, I think. Often it's less. Depends on the mission designer of course. P.S. did we mention the mission editor? It's pretty awesome.
The game has time compression so you can accelerate time as much as your PC can handle, so if you do find yourself in an uneventful flight you can whiz through it pretty quickly. That said, the flight dynamics are such that for a long time you'll probably just enjoy flying around even in the 'boring bits'. :)
Others have mentioned it but just to reiterate, the startup procedure only takes a few minutes once you're used to it - beginning the taxi on the 5 minute mark is pretty common, even with all the DSMS profiles configured to my liking. This is actually one of the nice things about the A-10 -- the startup takes long enough to make you feel like you're starting up a complex jet, but not so long you're sitting around waiting for 5-10 minutes with nothing to do. The only thing you need to wait for is the EGI alignment process, which only takes 4 minutes - and there's enough to do in the interim that you often don't need to wait at all.
Your typical mission will probably take about 1 hour to 1.5 hours w/o time compression. Some can be shorter or longer obviously, but I think that's pretty indicative of the average length. It doesn't seem like very long when you're flying it... and you can pause if you need to attend to something else.
The game does have a track saving system whereby it saves what happens in a mission so you can watch it later, and it's possible to take control of a track you're watching at any point. However the system sometimes misses events making it pretty hit-and-miss - the longer the track plays for the more likely it is to diverge from what actually happened. So, to some extent you could use that as a "save" system (i.e. quit, save the track, then later replay it and take control near the end) -- but I wouldn't rely on it.
A bigger issue (for me, anyway) is one of continuity. I don't really like playing runway-start (let alone air-start) missions because starting up the jet, taxiing, takeoff, and flying the ingress is all part of establishing the mood of the mission. Without them I feel like I'm missing something. Therefore while being able to reliably save and resume sessions would be useful at times, I'd personally use it very sparingly as it'd just kill the immersion.
Finally, another ++ for TrackIR. I've got the v4 and v5 hardware and there's not really much difference, so if $$s are an issue and you can find a TrackIR 4 for cheap I'd go with that rather than a 5. Depends what other hardware you already have - a good HOTAS is a must, and I'd get rudder pedals too if you don't already have them (not really necessary for the A-10 but still definitely nice to have).