The only thing that you actually need right away is a set of dies for whatever caliber you're going to reload.
If it's a bottleneck case, you'll probably need a way to trim them from time to time. Lee makes some cheap ones. If it's straight walled pistol cartridges that you're reloading, trimming probably won't be necessary.
Having a way to clean cases can be important, especially if you plan to switch to another lube later. The one that comes with that kit is water soluble, so you can just toss the cases into a container with some hot soapy water and give them a good shake/stir. The best option is a wet tumbler with steel pins like the one Frankford Arsenal makes. Again, if you're using straight walled cases (and carbide dies, which are pretty standard for those cases) then you won't need lube and cleaning is 100% optional unless they're muddy or something. Just a quick wipe with a rag will do fine.
A digital scale is nice to have to double check the case weight before/after adding powder just to be sure. I use this one and it's nothing fancy, but it gets the job done and was cheap. Otherwise you can also dump powder onto the scale that comes with it. Some powders are super fine and bounce around a lot, so I try to avoid that.
And there's a never ending list of other things that you could buy. Just keep in mind that people got by just fine using these for many years with no other accessories other than a hammer and a rag for wiping cases. It's up to you to decide how far down the rabbit hole you want to go!
EDIT: Oops, almost forgot. A good pair of calipers. I prefer digital because you can re-zero it at any point to measure a different in distances. But dial calipers work too. You need a way to measure the finished cartridge to make sure the bullet is seated to the correct depth.
Hornady s digital scale for 60 - is good enough to trickle on Or Maxus off Amazon for under 17 bucks - as long as you don't trickle on it is rocks. It does fluctuate +/- .04, but that's because it goes to the 100th where most go to the 10th decimal place, so when you find it to the 10th as we always do in our charge weights, it's spot on. I've tried a bunch of other ones recommended by people and these are the only 2 that I didn't find to be flaky.
Maxus https://www.amazon.com/dp/B07ZQZ962K/ref=cm_sw_r_apan_i_NWEDFTKR4T8C76TBJBE1?_encoding=UTF8&psc=1