A tumbler and media is definitely not necessary. Especially if you are constrained in space, and a wet cleaner is expensive. A plastic gallon bucket with a big plastic spoon and dish detergent will do the job, drying out in a oven at low temps. I've done a few thousand cases that way and it works fine and expense was less than $5.
Calipers, yep. Forget that Lyman case gauge thingy, it is inaccurate at best.
Lee die sets, they work for me and they are very reasonably priced.
L.E. Wilson/Dillon type headspace gauges for rifle calibers for sure. I use them for pistol also but your pistol barrel will make a great gauge too.
Need to trim rifle cases and the Lee Precision Case Length Gauge method is cheap and it works, if you ever start shooting a lot of 223/rifle it will get old and a lathe type crank trimmer or some other faster method will be desired.
Read up on case lubing, I prefer the pump sprays.
The little hand tools in the kit(debur/pocket cleaner) are serviceable, but not outstanding, you'll not likely be worrying about primer pockets in 9mm anyway. Some primer pockets are crimped, military rifle and sometimes 9mm comes that way, you'll need a way to remove them if you run into some. There are cheap reamers you can buy(a knife blade or screwdriver will work, even), or expensive swagers.
LCT turrets are cheap, an extra or two will be handy.
Get the double disk kit so you can stack them for big rifle powder drops.
The Lee scale is precise, but possibly frustrating to use. If it works for you fine, but if you start hating I'd suggest another beam scale like an RCBS 505, the Dillon beam, or on a budget the Lyman Pro-500(light but a chunk of lead hot glued underneath makes it a great scale, same agate bearings in it as the other reputable beam scales.
Electronic scales make me nervous, I've seen nothing good out of my 'my weigh', I weigh bullets with it.
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{don't over tighten the screws}
