Race/Roll for the Galaxy, Jump Drive, New Frontiers: Where to begin?

Oh man, this is my question!

I own all of them except for Jump Drive (which I have played), so I can give you a short answer and a longer answer. In short, they absolutely hold up in my opinion, they are all good to very very good depending on your tastes, they share a lot of concepts and symbology so once you know one its really easy to pick up others, they also tend to not stick if you are picking them up cold without someone to teach you.

1. Race - the classic. I have played this game more than any other in my collection probably (especially if you consider the app version which is phenomenal). I first tried this game very early in my boardgaming career many years ago and bounced off it as it didn't click at all, and it basically felt like solitaire at the time. It wasn't until a buddy who loved the game taught me that it clicked. I then taught my then girlfriend (now wife) and she fell for it hard (and is now kind of a monster at it), we were abroad for our wedding and went to a boardgame cafe during that trip and actually played the french version of Race there and there were absolutely no issues (I still call Galactic Trendsetters: Trendset Galactique). The game is beautiful in it's simplicity, there is no writing on the cards besides their name so its language independent, and you can easily get through a game in 15 minutes and still have a deep satisfying experience. It can feel isolating, but the interaction comes in once you figure out it actually is a race and that you are trying to predict what action the other players will choose and try to read the table to figure out how you can benefit more from their selections than they are benefiting from yours (this is the common theme of the series). It is also a game where a 25 to 17 victory can be just as impressive as a 80 to 60 victory it just sort of depends on what your opponent is doing and what cards you see and can effectively use. My only complaint honestly is that as an engine builder it tends to be over before you can really enjoy your engine too much, but that just makes you want to play another game. There are a number of expansions, I tend to go with Alien Artifacts (but I don't use the extra mechanics, I just like the cards), in general i dont use the extra mechanics from the expansions. I also pretty strongly prefer Race with just 2 players.
2. Roll - This one also did not click with me the first time I played it (after the first time I tried race, but before I was properly onboarded to it). Roll is possibly my favorite of the bunch. It has a lot in common with Race, but the dice pool mechanic is a lot of fun and it has the most tactile and worker placementy feel of all of the games, we call it space yatzee sometimes. The dice placement gives the game a bit of a spacial element. Roll is my probably my favorite for larger groups, it tends to play in about 45 minutes or less, and gives you a bit more time with your engine which I like. I have both the expansions, but I havent actually integrated Rivalry into the game yet which I believe improves the two player experience (already quite good) a bit.
3. New Frontiers - this is RftG's Puerto Rico to Race's San Juan. This is the beefiest entry of the series with games easily going over an hour and often taking up to 2 for a full table. It has the most boardgamey experience of the lot and gives plenty of time to develop your empire. I like this game a lot, I have also played it far less than I have either of it's predecessors, but it is always welcome on the table. It does have some square edges, and could possibly feel a bit incomplete in a way that I am sure an expansion (upcoming) would address, but I would still recommend it without reservation. It is honestly probably the most accessible of the group for someone who is familiar with boardgames, but new to the series as both of the first two can feel like spinning your wheels if you don't really understand why you are doing what you are doing. FYI, the box for this game is larger than standard so if space is a big consideration for you, keep that in mind.
4. Jump Drive - I have played this once, I would play it again, but it doesn't really fill a niche for me. It is a much simplified version of Race that is a better family option if you need that. I could well see myself owning it at some point, but while it seemed neat it didn't really do too much for me.

I dont know what I would jump in with if I were approaching the series anew, but hopefully this is helpful for you.

I've played Roll for the Galaxy and New Frontiers. I much prefer Roll. Turns in Roll are taken simultaneously and cuts down on waiting. It's efficient and easy to learn. New Frontiers is clunky. The military strategy especially seems quite overpowered and gameplay becomes repetitive.

Race for the Galaxy will always be good enough for today's standards! It really is a classic.

But if you are completely new to the series then Jump Drive is the safest place to start. It's a simple but solid game and like you said it's reasonably family friendly. It is a great way to get used to some of the symbology. You may also find that it's all you really need, or that this type of game is not for you. At worst you are only out of about $20.

All of the games are available on BGA and some also have apps. If you are open to experimenting with the digital versions then Jump Drive on BGA is the first thing I'd try. Next I'd try the Race for the Galaxy app (would start with the app in this case because it's easier to experiment there while learning).

One more game worth considering is Res Arcana by the same designer which is also playable on BGA. It's another take on some of the ideas of RFTG. Plays quite differently but shares the race to the finish aspect.