If you want a single stage kit, I'd go with this one:
MidwayUSA - Lee Challenger Breech Lock Single Stage Press Anniversary Kit
In addition to the kit, you will need:
-Dies for each chambering you want to load ($25-$35 a set on average)
MidwayUSA - Lee Carbide 3-Die Set 9mm Luger
or, if you want to seat and crimp in separate applications (which I like, but takes longer on a single stage):
MidwayUSA - Lee Deluxe Carbide 4-Die Set 9mm Luger
-Extra breech locks for the press if you are loading more than one cartridge ($8 per box of 2)
MidwayUSA - Lee Breech Lock Quick Change Bushings Package of 2
-A loading manual ($12-$30, depending on the manual, the Lee manual is the least expensive and has a lot of information)
MidwayUSA - Lee "Modern Reloading 2nd Edition" Reloading Manual
-A set of calipers ($15-$30, depending on brand and digital vs. dial)
MidwayUSA - Frankford Arsenal Electronic Caliper 6" Stainless Steel
-A bullet puller, for when you mess up ($15-$20)
MidwayUSA - RCBS Pow'r Pull Impact Bullet Puller
That should get you going. There is plenty of optional stuff, and you might want to consider some way to clean brass, such as a tumbler.
Then you just need components (primers, powder, and projectiles) to go with your saved brass. There are plenty of options with 9x19mm. I like Hodgdon HS-6 for it, but Titegroup, W231, and many others are also good powders. Pretty much any small pistol primer will do for 9mm (and get what you can find right now), but avoid magnum primers. In my experience, small pistol magnum primers work fine in larger cases, but in 9mm they can cause significant pressure and velocity increases over standard primers. As for bullets, I really like Missouri Bullet,
Missouri Bullet Company. Unless you are totally against shooting lead, go with them. They are inexpensive and good quality, plus they have excellent customer service and very fast shipping.
As for the apartment issue, I just bought a house last year. I started handloading in 1994, and from then until 2008 I handloaded in various rental property, apartments and houses over the years. I don't see any reason not to do it, so long as you have space.
I would not attempt to cast boolits in an apartment. I just took that up myself this year, now that I have a place to do it.