yes you can integrate realex with anything you want, but the complexity can depend on the cart.
as you say doberden, the advantage of the ones you list is that realex have plugin scripts that make integration very easy. although, if you want things to work a bit different than usual (e.g. less screens in the checkout process etc), it would of course still involved some customisation.
as for which cart to go for, it really depends on your needs doberden. how many different types of product will you be selling, how complicated will your shipping costs be, how much detail will you need to enter for each product (e.g. just a name, image and price or will there be size, colour, finish variations etc)....
also, are you constrained by your hosting package? of the names on your list, i only have direct experience of oscommerce, but i have taken a quick look at a few of the others in the past and afaik some of those ones are PHP/Linux based and others are Windows/ASP based.
oscommerce is very popular, and a lot of web hosts offer an easy install for it. there are all sorts of plugins available for it and it's free. however, i'm not that keen on it myself. it is quite bloated, and the admin area is not that intuitive. i don't do many shops, so i can't recommend any particular software i'm afraid, as i have usually coded custom solutions.
many shopping cart sites have an online demo available. your best bet is to try a few out. think of the things that you want to be able to do easily (add products, set up your shipping etc) and try them out. also, drop by their support forums if possible and gauge how active/content/helpful current users seem.