Will this speaker work

You cannot connect them with just an RCA cable because you need a phone stage/preamp between the two.  

Okay thank you, do you have any recommendations for decent ones that arent too expensive, and is it as simple as plug turntable into the preamp then plug that into the speaker?
Also what are all your experiences/opinions on using an active speaker like this for vinyl? Will it have that bad of an impact on sound quality?

Emotiva has a descent phono preamp xps-1 that retails for 199. If you could find a used one probably go for about 125 I would guess. 

There is a Rega Fono Phono preamp on ebay for 150 obo. 

Okay so I've had a little look about and was thinking something like this:
Turntable - Pro-ject debut carbon evo
Pre-amp -  Rega Fono Mini A2D Phono Pre Amplifier https://www.hifix.co.uk/rega-fono-mini-a2d-phono-pre-amplifier-black-new-version?gclid=Cj0KCQiA0fr_B...
Pioneer DJ DM-40 Active Speakers
Pretty sure this will all work together just wanted to make sure. If anyones had any experience with any of these I'd be interested in your thoughts. Hopefully in the future if I have a bit extra money I could replace the speakers to a passive + amp. Thoughts on the set up?

You've fallen into the trap of thinking more is better. In reality its not until you get to a budget orders of magnitude greater that separates start to make sense. Maybe not even then.  

Your turntable choice is fine. What you need from there is a phono stage, amp, speakers, and wire. The best most cost-effective approach is an integrated amp, preferably one with a built-in phono stage.  

There is by the way a very simple logical reason why this is so much better. By far the greatest part of the cost of any component in your price range is the chassis, knobs, etc. Within the chassis one of the biggest cost parts is the power supply. Needless to say the chassis isn't that important to sound quality. The parts used definitely is incredibly important. So an integrated amp with pre-amp, amp, and phono stage all in one chassis saves an incredible amount of money that the manufacturer can then put into better quality parts. No wonder when you compare them the integrated totally sounds way better than whatever else you can buy for that same amount of money. 

This is even before considering interconnects, which make a big difference. Get them all in one and you only need the one wire from the turntable. Which if you're smart you buy a turntable with the phono lead hard wired so you don't even have to buy an interconnect. Make sense? 

The active speaker is a version of this philosophy. It saves money by using the speaker cabinet in place of the amp chassis. But there's a couple problems here. The amps tend to be specialized for the frequency of the drivers or impedance of the speaker. Which is fine. Except the real reason they do this is to get away with as cheap parts as possible. Which is bad. And the amp winds up being in the worst location you could possibly imagine, right next to the high magnetic fields of the drivers and the vibration they produce. Finally, when later on you want to upgrade then you find your choices limited by these crappy amps built into the vibrating speakers. A good integrated is a far better way to go. 

There's a ton of em out there. What's your budget? With a $500 turntable I'm guessing $2k all-in? Something like that? Whatever it is, divide by the number of components you need- integrated amp, speakers, wire- and go shopping!

I’ve a Quad Vena II integrated amp. It has phono inputs, but when you get bored of those same LPs on your turntable it has a built-in streamer. And coax and optical digital inputs if you want them in the future. It does Airplay, and Bluetooth if you use it. Bonus - I think it sounds fantastic.  It’s the Swiss Army knife of amps. 

Quad Vena is great recommendation. Look no further, I suggest.

You’ll need the Quad Vena II Play for phono AND streaming.
It is one class beater package for <$1000.
Everything but Qobuz from what I see.
If you like 40kbps it has SiriusXM.

That Quad Vena looks amazing! Not sure if its quite in my budget though, I might try and find one on ebay a bit cheaper if I can, if not there seems to be a few alternatives available. So if i stick with the project carbon and manage to find an integrated amp all I need is a passive speaker I believe.
The JBL JRX 215 seems to have some good reviews at a decent price, again I am open to suggestions. Most of what I play will be Indie/Rock/Metal which I know can influence the speaker choice. 

The Quad Vena looks great but think I'd have to try and find one second hand due to cost. Was looking at the Denon PMA-800NE as a slightly cheaper alternative. 
Still struggling to settle on a speaker as I'm not entirely sure what to look for. Also I am unsure on what the power output on them means for compatability, for example the Denon puts out 85W per channel whereas the JBL speaker says 250W. Does this mean they cant be used together and if so why (just out of curiosirty)? 
Connection wise can I just use standard cables like RCA and whatever else comes in the box, I've seen a few people mention buying specialised cables which sound like another expense but I'm not sure if theyre necessary?
Feel like I'm asking a lot of basic questions so sorry about that I appreciate all the feedback!

Hello Oliver!  Im a little late to the party and haven't read the entire thread so forgive me if I'm asking stuff thats already been covered.  

Whats your budget after your turntable purchase?  

If you are trying to just go active, check out Totem Kin Play ($750 new from tmr right now), Kanto Tuk, Adam T5v or T7v, Dynaudio X14a, Dynaudio Xeo 3.

Some of these have on board dacs some do not. Some will keep the signal all analogue which may be important for you since you are doing vinyl.

I'd look into Schiit Audio for decent inexpensive phono preamp or dac.