First of all, welcome to the hobby!
You can paint your army in any scheme you like. Marines in particular have special rules assigned to chapters in specific colours, for example, Blood Angels in red and White Scars in, well, white. but as long as you are consistent and are clear with your opponent, then if the scheme looks good, then people tend not to mind. People tend to get grumpy if they think that you have used a paint job to conceal something deliberately and will suddenly pull a sudden unexpected switch on them. Otherwise, counts-as is an important tool in the hobby box and tends to be viewed favourably.
For example, I don't know if this is even possible any more, but if you have an army with multiple detachments and each detachment is a different chapter, but you have them all in your own scheme and still want to use chapter specific rules, then its confusing and you'd likely hit some push back from opponents. Clarity is the key in my opinion.
Also your army doesn't need to match. The
40k lore is awash with examples of last-ditch forces coming together to work together, or long lost crusades that have been scavenging whatever they can to survive, or even just a normal crusade force with squads provided by different chapters, all working together in a single combat theatre. The Departmento Munitorum is not known for its communication efficiency, or for significant lead time in deploying forces, and therefore you can have ice-world armour still in its tundra camo schemes being deployed alongside jungle troopers in some kind of wacky red/blue alien flora camo. In other cases, a force will be properly equipped for the climate and environment it is being deployed to and all the regiments or chapters involved will have a consistent colouration. Its up to you.
Lo and behold, a purple/teal space marine:
Paiting bright colours over black is hard, and you will need to use multiple coats. also base coating of any kind I find to be demoralising and painful process, so I would recommend finding a spray-can that matches the main base colour you want to use, and build up from that, rather than black. Grey Seer is a very light grey, almost white, so that makes painting darker colours harder, and you end up with a very bright result. This is great if that is the look you are going for, but can cause problems otherwise.
Using a mid-grey is a handy go between if you don't want to use a coloured base coat.
There are loads of good painting tutorials out there, so definitely look them up to see what kid of colour combos you like.