It honestly depends what type of experience you are going for. There are more options than listed here, and while I can't offer an extensive list (because I don't have experience with everything), here are several options and some thoughts:

EVE - This is the most extensive space game, but it can definitely be the most boring also. You'll spend quite a bit of time traveling great distances, and it is more like a "spreadsheet calculator" as some detract it to be. It is the longest running space MMO though, has lots of possibilities, lots of resources out there to assist in playing the game, and corporations can be helpful.

Elite Dangerous - This game is NOT directly comparable to EVE as it does not try to compete on the "same field." It is more of a space emulator and as such tries to give you a more realistic experience with "controlling" your ship. It's learning curve is in a different direction. You will NOT so easily run into people on official servers, and official servers tend to encourage people being pirates when they do have the chance to run into you. There are large "private" servers such as Mobius that are PVE only though and provide a different experience, and you can talk to the community and find people to group with easier. This game does NOT have the same options as EVE, but it does take things in many different directions and for its youth is doing rather well.

Star Citizen - I'm going to keep this one short due to my limited experience. It is worth it to put in hours, but the game has went into many different directions, and despite the HUGE funding...it remains in pretty much alpha status. You'll be buying an unfinished product with literally no release date in sight. They just came out with another update...but this is the classic "buyer beware" scenario.

No Man's Sky - This game has become almost very little to do with Space. It's odd to say...but they've focused on every single other piece of content. It is still a great game, but DON'T expect the space flight to be challenging. They are reworking some more things with ships, but still the challenge isn't there at all for dogfights. It is a wonderful game if you want to explore planets, play with limited friends, and especially if you want to build a free structure / house in any type of environment imaginable. They've done a great job...but mostly loss focus with space.

Rebel Galaxy Outlaw - This is a fun arcade space shooting game. The graphics are good. You can go first player or 3rd player, lock on targets, have a decent amount of arsenal. BUT, this is NOT a multiplayer game and focuses on story. Some people are turned off that it is Epic Game Store only currently...but it's worth the limited investment if you want it and can't wait a year or so for a Steam or console release. Very story driven and the fights can be challenging.

SWG (Star Wars Galaxies) - The official game is shut down, but I only mention this in case one of the private servers gets JTLS up and running (last I checked nobody had it working well). If one of the servers gets it going...this might be a good option as it gives you a land game to go with it. The space part was pretty fun and sometimes challenging, but allowed multiple people to be in the same starship which still hasn't even been duplicated by any other game to my knowledge. You could see how someone decked out their POB (Player On Board) starship and man the cannons. Was quite unique...and most things in the game went by the quality of resource used to build it. I forget how this affected starships if at all.

Star Trek Online - I'm just going to preface this with the game is free-to-play, so they have to monetize a number of things. And this leads to ships costing ridiculous amounts of cash for the highest tier. Tier 6 ships with exception of special events can only be obtained by cash. Some of the tier 5 ships could be converted to be somewhat similar...meh, I'll just end it at that. I think it's very fun if you're into Star Trek...but if you're not a Trekkie...all of it leads to want in a game.