Each time you level up in Galaxy Legion you get 5 points to spend upgrading your ship in some way. There are 6 different things you can spend these points on and unlike most Facebook games there isn't a strictly correct choice between them. There are a couple duds but there are 3 top tier choices that lead to different play styles. You can get cargo space, ship size, attack, defense, energy, or research.
Cargo space increases the size of your cargo hold by 5. This lets you hold 5 extra artifacts, or 50 extra minerals, or extra modules you aren't actually equipping on your ship. In some games this would be a good way to increase your income (in the game Gazillionaire how much money you could make was directly related with how much cargo space you had) but that isn't the case in Galaxy Legion. The mineral system is a way to seamlessly increase income as you level up and to give slight discounts on purchases to people who plan far enough ahead but having more cargo space really just means less button clicks for minerals. Being able to carry around extra stuff provides some level of flexibility but it's not that impactful. Cargo space is the sort of thing where you _need_ enough to store a basic amount of stuff and any beyond that is just convenience. There are two different artifacts that increase your cargo space as well as some mission rewards that do so as well so you're not stuck buying it with rank points. I suspect everyone who starts out spends a few points here to get up to a decent size but it's not something you're going to sink all your points in. Unless you're Honest Bung and are trying to corner the market on everything...
Ship size increases the size of your ship by 1. Ship size does two things: it increases the amount of damage you take in combat and it lets you equip more stuff. There's a plethora of random modules you can earn from missions and from killing NPCs that you'll want to equip on your ship. As you research better stuff in the different research trees you'll find that the size of those modules also gets bigger as well. Until you get to a very high level you'll always be able to get some benefit from more ship size as there's bound to be something you don't have space for right now. Focusing on ship size is a very strong strategy, and is the one recommended by many veterans on the forums and the wiki. It's important to note that having a bigger ship doesn't really make you much better at any specific task but lets you be more versatile and do lots of things with the same ship setup. (I can equip all of my scanners with my ship, doubling its size wouldn't make me any better at scanning but would let me keep guns or armor equipped while scanning.) There is an artifact you can get with artifact points to increase this value as well along with a few NPC drops. One downside to ship size is if you're really into raiding disabled ships. Success chance there is based on crew size, which is the next 4 categories combined. Spending your points here instead of on one of them will make you worse at raiding.
Tactical officers give you 2 more attack. Note that very quickly you'll have weapons with a better space to damage ratio than 2 to 1, so getting ship size is better than getting tactical officers while you still have more guns to put on. Once all your guns are on, though, tactical officers is the only way to get more attack. Want to be the best planet invader around? You need tactical officers. Want to do the most damage possible to other players in pvp? You need tactical officers. Pvp in this game tends to center around people near your level and someone who has tactical officers has a huge advantage in those situations. They'll tend to have a smaller ship so they'll take less damage and deal more because they have a higher attack. There is no other recurring way to get tactical officers than by spending rank points. (And there are ways to lose them! You start with 5 and I'm down to 3. I think Mike has none at all.)
Helmsmen give you 2 more defense. This sounds analogous to attack but it's actually a lot worse for a few reasons. Attack is useful in planet invasions, ship defense is worthless. Attack increases the damage you do which decreases the amount of energy you need to spend to kill enemies. Defense decreases the damage you take but you have many ways to heal to full with the press of a button (and some cash) so it doesn't really do a lot. Stacking on more health can be just as effective (or even more so) though I don't really think either is very good. Defense certainly has a place in reducing how often you need to repair but the key is you never need to max out your defense. Getting more ship size so you can equip more defenses is probably a better way to go. And finally there is actually an artifact that gives you 3 helmsmen so even if you felt like you needed a little more defense you're going to get it for free eventually.
Engineers give you 2 more max energy. Max energy is relevant when you're away from the game for a long time (so it has time to charge to full) or when you level (you get reset to full energy) or when you use an item which restores your energy to full (you get one of these once a week or so). Having more energy means you get to do more things. You can shoot at enemies more frequently. You can complete missions faster, getting the rewards faster. You also just flat out level faster as well. Leveling up gives you more planets to colonize which increases your income, artifacts, or research. It also puts you into pvp combat with higher level people and your ship rates to just be worse than theirs. Personally I decided artifacts were awesome when I started playing so I've put a premium on leveling up and therefore have spent most of my rank points here. I definitely level faster than most anyone else but am pretty bad at pvp. Fortunately if they aren't online I can just shoot them a lot of times if I really want to shoot them, and I can afford to do that since I have a lot of energy. I figure I make 284 energy per hour. 51 of that is from my constant charge from relays. 22 of that is from ship modules that add max energy. The remaining 201 comes from my 1935 engineers. (The effect they have compounds on itself. I level faster because I have more max energy and because my energy refreshes when I level I get my bigger energy pool more often.) This makes me feel like I need to keep spending all my points on engineers even though my ship is starting to get awfully cramped. There is no recurring way to get more engineers other than with rank points.
Spending a point on scientists give you 3 research per hour. I really don't know how to compare this to the other options. More research lets you get better ship modules, though you will need more ship size to make proper use of them. You can get a new planet every 4 levels and my typical research planet is worth 150 research per hour. Spending 4 levels worth of rank points will get you 60 research per hour. The big thing, I think, is eventually you cap out on research when you've researched everything in the game. All the other options (well, except maybe cargo space) keep providing their benefit over the whole game. The research seems like it will eventually tail off and you'll wish you had anything else. Possibly you could forgo ever colonizing research planets and just get artifacts and mining but I don't know that you'd really find enough good artifact planets to make that work out. Also, you can get an artifact with artifact points to get these.
Most people will focus on one of ship size, attack, or energy. I started off with a ship size focus but once my ship got big enough to hold all my guns I switched to energy and never looked back. I think that was the right plan for my style of play where I just want to get my numbers bigger. I level faster than I would under another plan and I get to complete more missions. I also focused heavily on artifact planets which has let me make up the gaps from having a relatively small ship size. (Artifact points can permanently increase max health, defense, ship size, cargo space, research, and give you more rank points.) But just because this was the right plan for me doesn't make it the strictly right plan which makes me happy with the game design. Someone who focuses on attack will have a different experience than I but they'll really get to blow dudes up which probably makes them happiest.