You really do need a loading tray. They are necessary and make things go a lot smoother by eliminating spills, but more importantly by providing an organized lay out by which to inspect powder charges prior to seating bullets, a must. My first loading tray was home made and I still use it along with my more expensive trays.
And tumbling is never a bad thing, it helps in identifying a bad case, but by no means a must. HBF has inexpensive tumblers and media. When I first started reloading, I didn't tumble my brass for the first couple years, and accuracy was stellar. I just cleaned the lube off with either soap and water, or alcohol when I could afford to. So for the time being, just make sure you inspect the brass for debris inside, and make sure you get all the lube off and out of the case, other than that, you'll be just fine.
I would most certainly pick up a scale. Verifying powder charges is a must, in my opinion.
HF also has $10 dial calipers, so I would pick one up. I find this aspect important, and especially so when loading high pressure AL cartridges.
Other than those few items, you should be just fine for the time being and can add to your tools as you go.
GS