It's been a while since I ran or played it, so my memory may be "fuzzy," but the best spaceship-combat system I remember using was in WEG's (d6) Star Wars: The Roleplaying Game. That game had really good rules for both chases and dogfights, albeit (IIRC) they could get a bit unwieldy if the players tried to do "too much." But the whole system of "you can take multiple actions in a round in exchange for accepting a penalty to all of them" seemed to be both balanced and manageable (up to a point).
I can't recall the specifics, and unfortunately my copies of the game are in storage. Does anyone remember the details?
1E used 4 ranges - Point Blank, short, medium, and long. Point Blank isn't normally available; it's described, but not one of the allowed ranges.
3 steps:
1 Declare Actions
2 Resolve range action
3 Resolve other actions - one per each with actions remaining, in descending roll order. (Everyone rolls at once)
Repeat step 3 if more than one action is taken. Note that the ship may only make 1 movement action
in step 2, if both declared close, then close one band; if both declared open, then increase range one step. If one says close and the other open, opposed speed+Pilot rolls, winner decides. If one did nothing related to speed, the other determines change. While not stated as such, most GM's also allowed "hold range" as a movement action, which opposes close and open attempts.
Note that Torpedoes only work at short range, but have massive damage.
Blasters can be used at Short (diff 10), Medium (diff 15), and Long (diff 20).
If you declare an evasion reaction, you roll Maneuver + Pilot, and add to the difficulty to hit you but only for attacks in that pulse of step 3.
If you declare a shield reaction, roll against a TN by range (S=20, M=15, L=10), and if successful, the shields code adds to hull for resisting the damage but only vs that one attacker.
It works best when one side has only one ship; squadron-on-squadron is very awkward in this version.
Note that I was looking in the book to write this; if you remember differently, that is probably because the Rules Update and the Rules Companion change this.
2E is further different, and 2R&E is different from that.
Plus, there's also the option of using the Star Warriors board game.
Note that 2E presumes use of minis or tokens, and the various movement actions are not rolls, and ship speeds are fixed numbers, not die-codes.
