yeah your going to want a more 'touring' style bike, which is a road looking bike (skinnier tires, drop bars etc.) but puts the rider in a more 'relaxed' riding position as opposed to a racing position. also, touring bikes are made to accommodate racks, bags and more water bottles. basically they are made to carry more stuff and go longer distances. (more info:
http://en.wikipedia.org/wiki/Touring_bike). that mountain bike, and 90% of the mountain bikes you see these days are heavy, mass produced junk and most likely will leave you at more of a disadvantage. stay away from em.
honestly, i'd say the best thing to do is sit on craigslist for a few days looking for a good deal on an older road bike (aka '10 speed road bikes'). these usually have a more relaxed riding position similar to touring bikes and can accommodate racks. as a general rule, stay away from Schwinn's because there's a lot of lower end models (especially the Schwinn Varsity). also, a few things to stay away from that you can e-mail sellers ahead of time about: one piece cranks, cottered cranks, stem mounted shifters and bikes that are made of hi-tensile steel (aka gas pipe). bikes with this type of stuff are generally low end and will definitely give you more trouble than they're worth.
be patient, you should be able to find a good deal. in my experience, a lot of bigger local bike stores will take a look at old bikes and just tell ya 'i'll sell ya something way better than that junk'. don't listen to them! at the same time tho, you want to be careful and not dump a tun of money into an older bike.
a few basic things you should definitely replace tho: tires/tubes, cables, handlebar tape. if the bike is somewhat beat and looks like it needs a tune as well as the stuff i just listed, don't take it to a shop. they will over charge you. there's a lot of bike enthusiasts that just love to work on bikes. post something on craigslist about needing a tune up etc., and i'm sure some ol' nerdy bike dude will be willing to fix yer ride up for cheap. tell them your looking to do some touring/long distant riding, and i'm sure they'd help ya out.
good luck!