Any plumbing tips for a DIY maintenance novice?

Shower head, fairly easy fix if you don’t have to replace the stem going into the wall. And, even that is not hard as long as the line feeding it is securely attached. Can be a bit of a bear if it is loose and you are trying to re-insert one of those angled pieces of pipe into it.
If you are just replacing the head then no worries.
Faucet could be a pain in the ass. What kind do you have single valve? or three handle? I ask because the three handle ones seem to be more of a pain than the single.
If you have to change the entire faucet in the wall hire someone to do it who has the tools and knowledge. You can do it but you will not enjoy it and will in all likelyhood invent some new curse words.
If you can get by with just replacing the valve that is great.Remove the old one and take it in with you to be certain of getting the correct replacement cartridge. Also, check the brand name, they will ask and it is important.
For both all you need is a good Philips screwdriver and a couple of channel locks; although it wouldn’t hurt to have a pair of needle nose pliers handy to pull out recalcitrant parts.

It would help if you figured out the brand of faucet. Some are really easy to fix. Some are more difficult. I just fixed 2 Moen single handle faucets that had been dripping a little for over a year. Moen sent the replacement cartridges for free and included the tool – for free. They are guaranteed for life.
You need to know how to shut off the water before you do anything. I like to squirt some penetrating oil on things before I attempt to take them apart. I even spray the shut off valves. After a squirt I let everything sit for a while so it has time to work. (Sometimes I get distracted and it sits for a day – or two.) Then I go at it.

Make sure you have some of that very thin teflon tape. When you take off the shower head to clean it, clean the screw-on threads as well, with a brush.

Then apply the teflon tape over the threads. Screw on the shower head. You will cut way down on leaks.

You Tube has some great videos on how to do things. When I had to replace a flapper in a toilet I looked it up there.

I’ve got the tape from a previous job in the old house. Excellent reminder. The shower head attachments will probably need it. The shower head is one of those that is attached to the faucet itself and you turn just one piece on the right side to start the water and you pull up a button to get the water to divert to the shower head. As long as the water isn’t turned on at the tap part no reason to shut the main off for this initial fix I’m trying. The faucet part I am looking to replace is just on the little screen end where the water comes out and where stones or sand collect, not the actual mixer part. If it still drips and leaks and bothers me enough, I’ll take the whole mixer apart. I know where my water shut off is. Handy cupboard over the sink in the laundry room.

I’m going to end up going to the store and try to match the rubber washers. I’ll look if the pervious owners left any behind first in the utilities cupboard. I may have seen something in there. The kid who owned the place before me didn’t clean or maintain as I would.

thanks, @robbmarsh89 . I actually fixed the problem. It seems it was much easier than I thought. Seems my 11 year old son had been taking down the shower head and twisting it. He messed with the attachment to such an extent, they only needed to be reorganised and tightened. Oh the joys of raising boys.