Got a Blackstar Artisan 30, I play it through a Blackstar HT Distx and it sounds amazingly thick and warm. I only got one problem with it: on 'high' volume I get a lot of humming, and even more feedback. I can hold it back by turning the gain and/or the volume low, but I'd like to play without, or at least minimal background noises.

I was thinking of getting either a noise reducer, or a really good set of new cables. Does this help, and if it does, does it reduce my tone? Anyone have some feedback or tips on how to achieve this? I would really appreciate it.

You need to figure out what's causing the feedback first. What guitar are you using? Single coils and hollow bodies are going to feed back, especially if you are using a ton of gain, which it sounds like you are.
You can also do the pencil tap test for a microphonic preamp tube if you suspect the issue has emerged recently.
Cables won't help, really. They don't cause feedback.

Edit - is this the Blackstar with the EF86 channel? Those tubes are notorious for microphonics. Might want to grab a few spares and a tube dampener of some sort to take care of that part of the equation. If it's a head/cab it's a good idea to dampen the vibrations between the two by putting something soft between the head and cab, or taking the head off the cab completely.
I'm using a LAG Arkane 3000, tested the amp with another guitar though and still had the same effect. And it's been there as long as I've owned it, so the tap test isn't an option either.

The model I own indeed has EF86 on Channel 1. Channel 2 has ECC83s, but it wont really change the noise or feedback. It's a combo btw.

I indeed play with high gain, and it's mainly the volume that's causing the feedback; there's none to little feedback when I play on low volume. However, the humming is always present.

Any other options to consider?

Thanks for the help.