First and foremost, root that thing and put a custom rom on it that is free from your carrier's bloatware. I personally run Cyanogen mod on both my Thunderbolt and Nook Color. It's a great minimalist experience that uses minimal resources. Basically, its a almost completely stock Android that you can completely customize to your liking.
As far as apps are concerned, I know you said free, but I would recommend you try out Netflix and possibly Hulu Plus. Netflix has a free trial.
Free apps:
1) YouTube - You probably already have it but if you don't get it. It's a great way to watch YT on your cell. Way better then through the browser IMO.
2) FREEdi YouTube Downloader - Allows you to download YT videos as either a video or AAC or MP3 file right on your phone. Simply amazing.
3) TuneIn Radio - Listen to terrestrial radio stations from all over the world using your internet connection. I listen to very little modern commercialized music stations these days but I love being able to listen to the BBC and European electronica radio stations. You can even use your GPS to locate stations in your area.
4) Speed Test - Test your bandwidth speeds. I have a Thunderbolt on Verizon so I'm always testing and showing off my 4G speeds. I'm such a dork lol.
5) Winamp - I prefer the stock music player but WA is awesome for listening to ShoutCast. ShoutCast has some great Anime and Japanese J-Pop stations.
6) Opera Mini - My favorite browser. Super super fast. Great for times when you are stuck on a 1x connection.
7) Dolphin Browser - Great for when you want to view website as would on your PC.
8 ) Google Navigation - Pretty cool. Still not as good as a Garmin IMO but it's getting better all the time. It's fun to use.
9) Crunchyroll - I'm sure you already know them. They have an app for watching anime.
And crap. My cell just died and I'm too lazy to go to the car to get my charger. So I'll have to get back to you on the rest of the apps I feel are essential because I can't remember without looking lol.
I hope that gets you started.