Auroras are basically the starter ships-- its basically saying I want to pledge to this game but I don't want to spend to much money (Which is totally understandable imo) They can do everything, but they dont do anything particularly well and I've heard they have a fair amount of trouble when it comes to the PVP arena. If you simply want to "try things out" on the cheap. This is your route.
Keep in mind the arena is a separate cost from the ships (its 5 bucks to unlock) unless you buy one of the starter packages.
Each ship has variant ships mind you. There are like 5-6 different kinds of auroras-- some being flat out better in every way than others of the same type-- but not always so.
Mustangs seem to be basic fighters, not bone-crushingly amazing but better than the auroras. If you're really into getting into a "more of a fighter ship" but at a reasonable cost the mustangs wouldn't be a bad choice-- bit fragile due to balancing issues but not bad. Mustang Delta is a limited edition fighter (theyll stop selling them in the next week or two) (its better than the alpha/betas) (gamma and omega are race ships -- not really applicable). The Delta is about 80 bucks + 5 for the arena so you're looking at 85$.
Skipping that route, I've heard nothing but extremely good things about the avenger. I don't have one, but people rave about how pretty good it is at just about everything it needs to be. Its nearly unanimously recommended over the mustangs by most people. It'll cost you 60 bucks + 5 for the arena so 65$.
Then theres the 300's which start to get into specialized roles. From my understanding the 325a is the favored of the bunch in terms of fighting and holds its own against the others with a bit of skill involved due to it being kind of fast. 80 bucks + 5 for the arena so 85$.
Beyond those then you get into the super specialized ships like the hornet which is a pure dogfighter and pretty much eats the faces off everyone if they aren't careful. But they're also much more expensive $$$ unfortunately. Cutlasses are in this group as well being the pirate ships that they are, maybe dont carry the same amount of bite that the hornets do, but certainly not something you want to meet in a lonely dark alley way at night.
Most of the other ships are racers/industrials/ some weird ass thing not really worth mentioning if you're focusing on the arena combat for now.
I'd recommend the avenger simply because ive not heard a single bad thing about it and its within your price point.
One more point on the game being unbalanced. Because it super early alpha there is no ship tweaking via in-game items to adjust speed stats or stuff like that. So everyone thats paid more than you will have a slight advantage. However the avenger is middle of the pack and probably puts on the fairest terms with those above and below you.