Welcome aboard to CD Freaks.
As you mention you had DirecTV, I assume you're in the US.
To get started, I would recommend checking out what's available on each satellite, as you'll need to decide whether to start off with a simple fixed point offset satellite dish (80cm or about 3 foot) or a fully motorised large dish. Unfortunately, the dishes supplied by pay TV providers such as DirecTV, Dish network, Sky, etc. generally don't work well outside of their main satellite footprint.
The first satellite I would suggest looking at is Galaxy 19, which can be picked up on a fixed point 80cm (about 3 foot) dish in most areas in the US:
The dish and LNB you'll need is determined by the footprint of the satellite(s) you are interested in picking up. For most of the satellites, you can check the footprint by clicking the link in the 2nd right column on the Lyngsat satellite channel listing pages. Check your coordinates on the map and use the table to the right for the dish size required. Most of the channels listed are linked to their relevant websites, so it's worth checking them to see what content they carry. Unfortunately, you'll not get the major premium channels on free to air (e.g. Discovery channel).
- The frequency range of 3.6GHz to 4.2GHz is generally picked up with a 1.2m (4 foot) or larger prime focus dish (solid or mesh) and a C Band LNB with feedhorn.
- The frequency range of 10.7GHz to 12.75GHz can be picked up on an 80cm or larger dish on most satellites with free to air reception (in the US) and a standard offset LNBF.
- To pick up two or more satellites that you are within the footprint of, you will either need a motorised satellite dish or a monoblock LNB (for two KU band satellites roughly 6Â° apart).
Generally, you'll not go wrong with most PC satellite tuners, as the majority of them will work with most third party satellite tuner software. As far as I can tell, DVB-S2 only seems to be used by pay TV providers, so I wouldn't worry about getting an expensive DVB-S2 capable card until enough FTA broadcasts start up using DVB-S2 in the US.
I would also recommend reading this thread, where I had a discussion about picking up free-to-air satellite with a C Band dish.