As OB1504 said, it's not common you launch directly into a gate agent job. Most contract companies that handle airline contracts do both counter and gate work and you would do both.
I was one of the lucky few to hire directly into a gate agent role, though. I worked for SkyWest in SFO
as a UAX gate agent - we didn't handle lobby check-in at all because that was handled by mainline United. I found it quite refreshing and fun when I worked ticket counter positions temporarily at other cities.
When I went on to work temporarily with a ground handler in a supervisory role, we started out at the counter and then worked briefly at the gate. Because we had a single flight, most of the action does happen at the ticket counter. And that will be the same with pretty much any contract company you try and get on with.
If you're being Houston specific, the only contract company I've found with current openings is Menzies Aviation.
Other handlers in Houston that I'm aware of are Servisair (US Head Offices are in Houston) and DAL
Global Services (DGS). Delta Air Lines itself often does "Ready Reserve" positions which may be attractive to you if you're a full-time student.
Head in the clouds... yet feet planted firmly on the ground.