You'd probably enjoy contesting on HF, or just working DX. A lot of the DX stations don't like to ragchew much and just try to make as many contacts as possible. In many cases, a lot of them only know enough English to say their name, their location, what they're using to operate and 73! In contesting, like Field Day, speed is the name of the game. Some get really serious about Field Day and some clubs just do it for fun. Other contests like WPX (the SSB was this last weekend) , CQWW, ARRL DX Sweepstakes, etc are often more competitive. Those are the big ones. There's smaller ones like regional contests and the RTTY sprint etc. that are fun as well. Everyone can find their niche in ham radio, and it's not always sitting there shooting the breeze, either. Many just do CW or the digital modes, SSTV, satellite, just contesting or whatever.
You only have to be a Technician or higher class to work the satellites. Most satellites are 2m and 70cm, so techs can operate there no problem. In fact, its one of the best ways for no coders to work some DX! In some rare instances (PCSAT2 or AO51 in PSK31 SSB up mode) there is a 10m uplink, and the satellite portion of the 10m band is for Generals and up.