I'd recommend replacing the half nuts if there's any appreciable play in them. You can work around worn ones with a fair amount of backlash (I did for a couple years), but it will just make everything that much more frustrating. There's always going to be some backlash (or the screw wouldn't move), but dealing with minimal backlash is easier than a lot of backlash. You can still order new half nuts from Clausing and in retrospect, they should have been one of the first things I fixed on my Atlas.
Give the leadscrew a good inspection as well. If it's worn to mostly sharp points on the Acme thread, make plans to replace it. Again, you can work around it, but it makes many things a PITB that don't have to be. Last time I checked, Clausing still sold the leadscrews, but they're not cheap by any means.
Not much you can do about wear on the ways, but the worst of it will be within 3-5 inches of the chuck. that's where the majority of lathe work is done.
You can do good work with a lantern post, but it's so much more of a PITA than a QCTP.
I used the lantern for a while when I first got my Atlas, mostly to prove I could. Well, I also wanted to be half decent with it just in case I ever had something break or fail and I needed something to "get me through" until I could fix whatever was broken.
It was night and day when I switched my Atlas TH42 to a QCTP. Mine is a 10" so I use an AXA. So much easier to mount tooling, so much easier to get it on center. Adds a measure of rigidity too. Get a "wedge" style QCTP is you can swing it. A piston type is ok for hobby work, but a wedge is better, assuming you can part with a bit more cash.
The next thing I did was to add a DC motor and controller. Again, a leap of light years in usability. Most guys go AC with a VFD, I prefer the DC motor. But it is a more unusual direction than most that go with the AC motors. Different strokes for different folks.
Chuck. If it's not in good shape, get a new one. Even a no-name import is better than a well worn original. My preference is for an independent 4 jaw over 3 jaws or scrolls. Takes a little longer to learn how to use it but once you do, it's almost as fast mounting stock and you can mount odd shapes and still easily get them on center. I look at it this way: anything you can do on a 3 jaw/scroll chuck, you can on an independent 4 jaw. But there are things you can do on an independent 4 jaw that you can't do on a 3 jaw/scroll. You're trading off speed of use for versatility, but you also only have to buy one chuck. that's an important consideration if you're a hobbiest on a limited budget.
I also took the top compound slide off and made a solid plinth to hold the QCTP. What that does is remove another point where the lathe can "vibrate" or "flex". With the top compound, parting was a major frustration. Chatter, vibration, jumping, jamming etc. Even with all the gibs cranked right down. Once the plinth went on, parting became almost a joy. I used to avoid parting at all costs, now I just grab the parting tool and have at it without a second thought. I only install the top compound now when I need it for a specific operation (cutting bevels, etc). I use the plinth pretty much exclusively these days.
Change gears. Get yourself a set unless your lathe has the Quick change gear box. 3D printed ones work fine. I have a couple in the driveline of my TH42. Not because I was missing them, but because the plastic gears take a lot of the "ring" noise out of the lathe when it's running.
Get some lighting on it. Flexible arms are the best so you can put it right where you want/need it.
I mounted a small whiteboard on arms that raise and lower. Gives me a place to do some math calcs and/or write down a measurement so I don't have to try and hold it in my brain. I much prefer it to having a paper pad lying around which always gets oily, knocked to the floor, misplaced, etc. Velcro some dry erase markers and a digital calculator to it as well and you're good to go.
MOLO. Manual of lathe operations. It's the stock Atlas users manual. Tells you everything you need to know about setup, maintenance, adjustments, lubrication, screw pitches, etc. It's also written in fairly common English, so the average guy can understand it. Not a lot of machinist technical terms and subjects, but plenty to get you up and running. Lots of options to download it in PDF, or you can buy a paper copy from various sources.
Get a drill chuck on the proper MT for the tail-stock. I like the older Jacobs chucks that were USA made (with a pref for superchucks). But they're all old and worn by now and rebuild kits are expensive and hard to find. New Jacobs are all built "overseas" these days, so just get something the best quality you can afford. I find keyed or keyless doesn't mater much to me. I actually have a pref for keyed chucks. I'm just a "Traditionalist" I guess.
The rest is down to the actual tooling you want/need to do the jobs you want to do. Off the top of my head: left and right cutters, parting tooling, boring tooling. You can start with grinding your own HSS blanks for the various tooling uses, or you can go to carbide inserts. I use both. My turning tooling tends to be carbide inserts as is my boring bars. My parting tooling is nearly exclusively HSS. I do have carbide parting tools, but I find them harder to use, has shallower reach and they tend to catch and break on me.
At least start off with HSS tooling. You need to learn how to grind them properly, even i you do decide to go to carbide insert tooling. There are times when you need to grind a special profile tool and if you at least start out with HSS blanks for tooling, you'll develop the skills to make those special shaping tools when you need them.
Steady rest is a great addition if you can find one at a reasonable price. Center drills and a live center and a dead center are also fairly essential if you do anything much longer than a few inches away from the chuck. A follower rest is fantastic, but they're hard to find and expensive when you do.
He's a snap of my Atlas TH42 as it sits, you can see some of the stuff I was talking about:
The rest is mostly greases and oils, which the MOLO will tell you what you need and where to put it.
You'll need oil cans. I prefer the old "Eagle 66" cans:
Quality pieces. Easy to control, don't drip and the tips are sized perfectly to depress the ball oilers on the lathe and squirt in the oil. You don't need the ones like I have, but they do go nicely with the looks of an older lathe. Whatever you buy, make sure it's good quality or it will be frustrating to use and leave drips of oil everywhere you put it down.
Anyways, I think that's enough to get you off to a decent start. Or at least it will dent your wallet well enough to make you want to take a little break from it for a while.
Cheers