I personally would just go with a rosehair tarantula (
Grammostola rosea) based on your criteria; they're cheap, readily available, & are very calm tarantulas that can be handled. They are terrestrial and also tend to not burrow in captivity, so you would be able to see it all the time. Another good species to look into is the pinktoe tarantula (
Avicularia avicularia); they're arboreal and can be handled although some specimens can be a bit jumpy (nothing major, though). Keep in mind that tarantulas are often sold as spiderlings a.k.a. slings, and they must be grown out in a smaller setting that their adult enclosure; some species grow incredibly slow while others grow fairly quickly, so be sure to do research on the specific growth rates of the species that you're looking at.
Another fun way to start is to order a tarantula grab bag from a vendor such as
Ken the Bug Guy; you just need to mention that you're a beginner, and he'll send you a nice variety of species that would work for a new tarantula keeper. I was very pleased with the grab bag that I got from him, and I ended up with tarantulas that were worth way more than what I paid, so it's definitely worth the money, too.
As far as care goes, you would only need a standard 5 gallon aquarium for the smaller species that were mentioned or a standard 10 gallon aquarium for the larger species; the vase majority of tarantula species available in the trade will not outgrow a 10 gallon unless you start getting into the
Lasiodora,
Theraphosa, & the like. You would want to make a plexiglass/acrylic lid with a bunch of small holes in it for the lid rather than use a screen lid. Use a substrate that's a 60/40 mix of peat moss/vermiculite, and be sure to follow the guidelines listed on this
page for substrate depth & such. As far as feeding goes, just feed the tarantula(s) an appropriate-sized cricket or two every week when it's young for all speices and increase the number of prey items if need be when it gets older. In some cases, you will need to decrease the feeding frequency for certain species, e.g.
G. rosea, to every other week; obesity is something that you can run into with certain species, so you must keep an eye on the tarantulas weight & appearance. Roaches can be fed, too, but many tarantulas will not eat them; other food items are best to be avoided, especially mice & other rodents.
Hopefully that helps!