I'd keep the TV antenna. If it doesn't have the batwing attachment for better UHF/HDTV reception, I'd buy one of those as well - I think they're 20 bucks or so at Camping World.
Since you say you're going to use your laptop to watch TV, I assume you have a TV tuner card for it? If not, get one that has an easy external antenna connection. You can then connect it to your TV antenna from inside your trailer and use the built-in booster in your antenna and the directional aiming of the roof-mounted antenna. You'll get much better reception than from inside the rig.
For cell phone - Wilson (and several other manufacturers) make a wide range of boosters. I've used a number of different ones with very good results. The system typically has a roof-mounted antenna (magnetic or permanent mount) a signal booster/amplifier (that can run off 12V) and an internal antenna, or a wired connection to your cell phone. My recommendation would be the internal antenna model as hard-wiring to cell phones is a nightmare of different connectors, wires, and inconvenience. Also, the internal antenna is generally a small piece of black plastic on a wire that you can hold next to any device you want to boost - cell phone, 3G wireless internet card, etc. Our current system has a VERY low-profile antenna (a hockey-puck about 3" high and 2" in diameter) mounted on the roof. It works quite well.
Since you're trying to be minimal, if you're not already using a 3G (or 3G/4G card) with the laptop - that's a great way to go for internet connectivity.
We did several of these things recently, and I wrote about them in a blog post:
Getting Connected - Riveted
Your FM is most likely connected to a rubber ducky antenna on the roof. I'd just leave that.