I was recently reading about primers which are mostly used for making sure foundation and makeup doesn't run. Obviously, I don't wear makeup, but they do appear to be good for oily skin. I'm not sure though if it's worth using both a primer and a matte moisturiser or if they just do the same thing. If it is worth a shot, what's the application process? Primer first? Moisturiser first?
Primers definitely help! I use it every time I put on foundation along with a mattifying moisturiser and when I don't use the primer, there is a huge huge HUGE difference in the way my skin looks. There are loads out there but if you just want to combat oily skin, any anti-shine or matte-finish primer will do. But I will mention the slight risk of getting break outs from it and makeup isn't one of those things that your skin "adapts" to really (at least not in my opinion at least). It has something to do with the silicone since most primers use that, but usually you just have to find the right one for your skin. Oh, and you moisturise first and then put on the primer!
Good luck and hopefully you find something that works for you 
I'm not fully convinced primers are necessary....they were invented as a way for the cosmetics industry to make more money, and also to improve the application of foundations that don't look good on their own.
I usually either use moisturizer or a primer, not both because it's unnecessary. I use cover fx's spf 30 primer because it has spf and it's supposed to control inflammation and nourish the skin. Not sure how effective it is, but it doesn't break me out.
I use benefit's porefessional primer and it makes a huge difference in the appearance of my skin. It is colored, but not enough to hide any blemishes, just a super light tint. It makes pores look invisible, skin texture looks smooth and after an entire day my skin looks matte.