I wouldn’t stop at 1-3, 4 and 5 still have the butt ugly tile graphics and keyboard only interface, 6 (plus spinoffs SE and MD) isn’t much better and even the mouse support is archaic and frustrating, 7 (including pt2) is just a mess codewise making it a bitch to run (and it always has been, even back in DOS days), and 8 and 9 well, anything done to those could only improve them really.
As a thank-you for bringing this up - I’ve downloaded it and spent the last couple of weeks playing it a lot - I’ll share my patented docking technique which I’ve now got polished up again after a 20-year break. Position yourself squarely in front of the slot (Oolite even gives you navigation lights to make sure you’re lined up), approach at moderate speed - still in the green but definitely not a crawl. Don’t try to synchro-rotate a la 2001 but as the slot is nearly filling the screen, you do need to start rotating. You shouldn’t need to touch the throttle now, instead use the pitch controls and the yaw controls to keep yourself pointing at the four lights. My over-50 reflexes struggled the first few times but I’m now back to sneering at docking computers as a waste of time and money.
I’ve already completed one mission which I never saw on the Amstrad version back in the 80s - it’s possible I’d left Galaxy 1 before ever getting the Constrictor Hunt mission back in those days. The missing ship’s a real bear to fight, but I got him in the end and was rewarded with 250 extra kills and some money (not really enough to cover expenses, but hey, the rating boost was worth it).
What I haven’t done yet is download any of the OXPs (Oolite Xpansion Packs). They look like fun. 
Dunno how I tuned out on this one, but I’m going to take this opportunity to once again plug Ultima V: Lazarus; Yeah, at this point, even THAT is super dated, but frankly, it’s 100% worth playing regardless. And I think they’re doing something similar with U6 which may or may not be shinier, since it’s still stuck with the same base engine. (Dungeon Siege 1. Erk.)
I have a bunch installed on mine and played a bit last night for the first time in quite a while. One OXP I use adds cops patrolling the space lane.
Jumped to Lave to sell computers and started getting harrased by a pair of pirates. Killed one (my first kill in Oolite!) and was having a difficult time with the second when a police patrol came in range.
I very much want to see the Gold Box games remade, but the Infinity Engine absolutely would not do them justice. I’d like to see improved graphics and (more importantly) an improved interface, but they would have to have turn-based combat.
If you’re rated Harmless and packing a pulse laser (the second pretty much guarantees the first), stay away from Lave, which isn’t a great trading base anyway. Nearby are Diso and Leesti, a Democracy and a Corporate who will happily sell computers and agri-products back and forth to each other and have fewer pirates.
You can also minimise traffic interactions if you take a detour on emerging from witchspace. Point yourself well above the planet and go into torus-jump a.k.a. hyperspeed. Adjust your direction as you get nearer. Most traffic is near the direct line from the witchpoint beacon to the planet so if you’re well off the track you’ll have fewer hold-ups (in both senses of the word) and get there quicker and unmolested.
You can always look for trouble later once you have an iron ass. 
Thief and Morrowind
Star control 2.
Though a word of advice to anyone trying to make a spiritual successor: don’t try to do the space combat in full 3D. Been there, failed to do that.
TIE Fighter. Please.
TIE fighter? Honestly, I didn’t even really enjoy this one the first time. There are lots and lots of good space sims past (for remaking) and present (for enjoying) and most of them don’t have the hilariously stupid TIE Advanced that basically breaks the entire game.
Why the love for TIE fighter over other space sims with more features, more balanced ships, and greater weapon variety? Is it just the Star Wars cult appeal?
Which is exactly what I was doing. Had been staying out of the space lane until I could afford a forward military laser, ECM system, extra energy unit, and shild boosters. Been working the Onrira/Erlaza run to afford a scanner targeting enhancement and recently ventured into short-range passenger transport.
Stunt Island was a blast but it was really pushing my machine at the time.
I liked X-Wing much better than Tie Fighter.
Incidentally, it was only a matter of time before I started meddling with OXPs. Mostly just for the ambience so far, although an improved sight did wonders for my gunnery. Now I have multiple planets, moons, improved planet, ship and station render, background chat near the station, improved sound effects… all the sort of things you can play with when you have gigabytes of memory and fast disc and sound cards instead of having to write miracles of machine code to fit things into 40k.
And being able to trade in your Cobra Mk 3 for another ship is fun, though it takes a lot of saving up before you’re ready for it!
A few more I would love to see:
Racing Destruction Set from the C=64 days
Interstate 76 would be fun with today’s tech
And I definitely second a Darklands remake!
Sword of the Samurai- I loved that game. I was still playing it (via emulators) up to about 2005 (IIRC).
I came in just to say Super Metroid. Nintendo has remade the Metroid games before (such as Metroid: Zero Mission), so it’s not completely out of the realm of possibility.
I’m wondering if they could possibly improve on Planescape: Torment with today’s technology. Other than more polished graphics, I’m inclined to say no.
Battlemaster was an old Genesis game that sometimes I feel I’m the only one who ever played it. It would be great as a remake.
So I’m doing a passenger haul from Tionisla to Beusrior. Arrived in Qutiri and encountered a pair of pirates, both with military lasers. Hightailed it back to the friendly Eagle Long Range that I passed near the Witchpoint and evened the odds.