I'd recommend both Macross Frontier and SDF Macross (It's English dub is the first part of Robotech). Both animes are top notch mechas with great story lines and amazing music. Frontier makes a lot of references to the rest of the Macross series (Especially to Macross 7, and surprisingly Macross II which was retconned [still good though]), although not catching them does not impede enjoyment of the show (I can attest to that, Macross Frontier and School Rumble were my first anime. After watching all of the Macross series [highly recommended] I re-watched Frontier, it felt completely different than the first time I watched it).
For comedies, I'd recommend School Rumble and Azumanga Daioh, both excellent Slice of Life comedies. K-ON! is another good SoL.
For a good Adventure/Romance/Economics themed anime, Spice and Wolf fills that niche excellently, with a strong cast, good story, and lots of economics. (To quote our lovable troll in charge of my university's anime club [somewhat based of a few of my comments while watching the show, and the graph I presented after] "This is the only show where I'd ever hear 'Inflation up in this ***** cheered at the screen'").
As for where to watch, I torrent, which is illegal for shows that have been licensed in your region, and a legal grey area elsewhere. You can use My Anime List as a resource to find who has fansubbed what, and if it has been licensed, dubbed, or if it is available on DVD. ANN (Anime News Network) is also a good source for what is coming up, what Funimation has liscensed, and news stories relevant to anime.