Everything up to Catacombs is free...so you can begin your subscription, upgrade to catacombs, New Frontiers (if you don't have that already)and Trials of Atlantis. You will not need to buy these...just start paying the $15/month and can upgrade whenever you want.
Classic servers are very popular, and good for a new person to begin at, but you are correct, they do not use the Trials of Atlantis areas, or major features from that expansion including Master Levels and Artifacts. For someone beginning the game, this is probably not a bad thing b/c you are very far behind the learning curve, and classic has less to conquer. Eventually, you probably will want to buy the last 2 expansions. You have to pay for them (Darkness Rising and Labyrinth of the Minotaur). you can do it from your billing section, and I believe it is $29.99 for both. many people say you can find the epic edition in stores or online for less than that though, and you would have to download less if you bought the actual discs. The downloads can be slow.
RvR is done is mostly done in New Frontiers. There are some smaller areas that all 3 realms have access to, but you probably won't spend much time in some of these (labyrinth being fairly popular and good for new peeps to go to, but you don't own this expansion yet). new Frontiers has keeps, and solos roam, 8 man groups roam, and often large zergs (possibly 100 people roaming as one large unit) roam around killing the other two realms. There is no instance RvR. There are battlefield objectives, but the main objective is killing enemies, and to a lesser extent capturing enemey keeps/towers/relics (but many do not ever do this and just roam looking for enemies).
Classes that are melee oriented, that also have some magic damage, off the top of my head would be:
Thanes (midgard)
heretic (albion)
Vampire (hibernia)
several others also have both capabilities, as all hybrid classes fit into this description somewhat, but those are probably the ones that actually can do some stuff with magic.