Welcome to reloading and thanks for asking our advice
Here is an essay I posted once elsewhere
thefiringline.com/forums/showthread.php?p=4731364
I think it bears repeating here.
Apartment Handloadng
While it is possible to load with a kit that you can keep in a shoebox, it is not all that convenient. The kit is the size of a paperback book, but requires a mallet to power the metalworking, which means you need a wood block, lest you dent your coffee table, plus it makes a lot of noise with all the banging and it is also slo, but can be benchrest accurate. If you are REALLY tight on space, it is one way to go. About $30-$40 for the hardware.
A hand press is the next step up in convenience. It requires no mount, but is not a lot faster than the mallet-powered setup. About $60-$80 for the hardware.
A small single stage press mounted with bolts and wingnuts to a 2x6 30" long is the way I started (though I do have a few sets of the "whack-a-bullet" kits and have used them, too.). I wedged the 2x6 into the drawer of an end table/nightstand and used it to great effect for a long time with a RockChucker press. Press, scale, dies and you can be set up in style for under $100 and still fit everything in a (deep) dresser drawer or medium-large briefcase.
Everything beyond the press, dies and scale just makes things faster, more convenient or moderately more precise. Highly recommended, but not ABSOLUTELY necessary. Of course, loading manuals, safety glasses and a dropcloth go without saying. For instance, you can apply case lube with fingers or a paper towel, but a case lube pad may be more convenient.
My current setup consists of a Lee Classic Turret and that same 2x6 I started with 35 years ago, seven sets of dies, a scale, a couple of powder measures and a number of other miscellaneous tools round out my loading bench. They all fit in three medium sized plastic toolboxes. Add a Stanley or Black & Decker folding worktable and I can set up anywhere (including going over to a friend's house) with just three trips out to the car (two carrying the gear and one carrying the components) I make more trips to the car preparing to go to the range. It would cost about $500 to duplicate my setup, but I want for nothing.
Lee Classic Turret Press
7 Die sets (all mounted in their own quick-change turrets
3 Auto-Disk powder measures (only two fit in my toolboxes, though)
Powder Scale
Powder trickler
bullet puller
calipers
Primer Pocket cleaner
Case mouth Chamfer Tool
Safety glasses (shooting glasses would do, but I keep a dedicated pair)
A set of Lee Powder Dippers
Tweezers and other small hand tools
A half-dozen loading manuals (don't keep them in the toolboxes, though)
Dropcloth (not in the toolboxes, either, but covering them
I think that's about it. Rifle shooters would have a few more items, as bottlenecked cartridges need trimming, lubing and such.
Good luck.
Lost Sheep