I'm new to this game (And when I say new, I mean very new - only rank 9). How should I invest my research points? As in like, cloaking, scanning, planetary building and all the others. I've only researched tier 1 for each. Which one should I make my main priority?

weapons and hull would be a good start imo

You are going to get lots of varied advice on this one. I know it is too early to tell right now, but please try to consider your personality and things like that. Those will greatly factor into how you play the game. Just answer these questions and it will give me and everyone else a lot better idea of what to suggest.
Are you a warlike (belligerent) person?
Do you enjoy killing other (pixellized) people or creatures in other games?
Are you more of a peaceful kind of person?
Do you enjoy more peaceful things, like doing missions? (I'm guessing that's all you've done so far)
Do you think you would like killing NPCs? (you probably already know this, but it stands for "Non-Playable Characters")

If anyone else can think of anything that would help, please add to it!

Well, I don't often attack people, but mostly when I do it's to hack to get research points. And yes, I'm a peaceful kind of person and I do missions and sell minerals to get credits. What I've actually done so far is scan for new planets and deciding which one should I colonise next. Just in case it's relevant, I'm a Sillixx explorer.

Attack first, then hull, planetary, energy and cloak.
PvP is needed to get the dom cannons, which are some of the strongest weapons in the game.
You'll need attack and hull for kills.
Planetary is to improve your production so you can get more research faster.
If you like missions, energy is key
Spend a little in cloak, up to around the third tier Sensor Jamming so you can hack as early as possible.
It also helps you stay off 99% of people BTs so you can keep your deaths low.

Scanning, base building and shields are not very important at your level.
Join a good legion, and the higher ranks will help you out with credits and planets.

Remember the game is for you to do whatever you find fun

I think scanning actually is fairly important at his rank, as he needs to have good planets.

If you like doing missions,

If you want to hack, then go a few tiers into cloaking. Cloaking is EXTREMELY cheap for a few tiers.
I hope this helps you!

As mentioned before, you'll get a LOT of varied advice on this. Here's what I'd recommend until you know what you want to make yourself: Research whatever the next cheapest tree is.

Not bad advice, actually. It's what I did as a newbie.

Planetary Construction, Advanced Armor, and Advanced Weapons are the research trees you should be focusing on.

I don't think he wants to do PvP. I personally loathe low-level PvP, although I have started doing it this time around at about R140 (I reset twice). It's a lot easier then in my opinion, because you don't have to worry about so many other things, like energy, funds, and artifacts (not a problem if you know people, but you likely wouldn't the first time around). The people are harder to disable, but it's better to me.
Back to my original point, there is always the reset button if he's not happy with what he's done with his ship.
I must agree, however, that Planetary Construction should be researched AT LEAST until +4s (Deep Extraction).

do weapons and hull then after a few months reset and you should have experience

Your planets are paramount, take care of them and everything else will fall in line

To that degree :
the planet construction tree is where you should focus a good majority of your initial efforts
Shields are how you defend your planet, but not worth putting on them until you finish the tree

Since you are peacful, you will want to put some research efferts into defense and cloak

scanners are important as they let you find more planets
***NOTE***
this does not mean that you will find "good" planets, just more planets.

Finding your self a good legion at start can also help out immensely especially in the research department.

If your ship does not currently have a place to call home there are some REALLY good 'training' - I say this because the players there know what they are doing, they are just low level - legions that are represented here on the forums that can help you alot. My legion is currently set to research as well, so you are welcome to stop by if you like. Anyway the galaxyways takes you I wish you well

Going a step further :
suggested missions : The Zolazin chain -> starts with the Glavez incident, or something like that.

reason : somewhere towards the middle of the mission chain, you will get 3 glavez devices they give you a free race / profession change. While explorer isnt a terrible proffesion ( much more helpful later on than at your rank ) Sillix is a 'trap'. The sooner you pull away from that race the better off you will be.

Definitely do planetary construction up to +4 to start with.

Go for scanners after that for a while, only until you have about 11 good planets (M/R for research VL/R (toxic) or VL/VR (volcanic) for mining VL/R for artifact) to last you up to rank 40. On the subject, don't defend these. You'll only be able to fend off noobs, who often don't invade much anyway.

Construction
>
Sensors
>
Energy

I say energy, because the low ranks don't have a lot going for them. Whilst you'll find people who're like "Oh my gawd, you should like so totally have all of your Dominion Cannon Mk3s by rank 100, you tool." that's completely unnecessary - particularly if, like you say, you're not into PvP much. By investing in energy, you'll be able to rank up from the low ranks and ultimately become stronger faster, and if you decide to PvP later, it's a breeze in the 200s, and still plenty easy enough in the 3-400s.

Once you've done energy, you can either continue down sensors+construction, or get some combat ability. Whilst there is some merit to the all-out energy build, ideally you'll have enough strength to deal with things like blockades (which cause you to lose production on one of your planets) and mission NPCs - as well as normal NPCs, often to find mission NPCs or T.O. Troop Carriers.

Obviously, I'm not saying do whole trees at a time! You can look at your opponents ship's to get an idea of what tech level they have, and forever try to 1-up them. That's often a good way of measuring what to research.

Anyways, if you need a legion, The Invisible Storm has a few openings. Our base is artifact based, which will actually get you more research in the long-run, than a research base.

I always advise to research weapons and hull and get 1300 red badges ASAP. You may not enjoy PvP all that much, but later on in the game you're going to want to get Dominion Auto-Blasters and it's easiest to save up the red badges sooner rather than later.