(a) What protoboards do people use? Is there an equivalent of the generic 2.54mm square grid -- something like pads without holes but in 1.27mm pitch? Does that even make sense, assuming I can largely stick with SOICs?
I always have a few 1.27mm, double sided proto boards available. Usually all square pads, with a few through-holes on one or all sides of the board so you can also solder connectors on or through-hole components, wires or whatever. You can find those easily. Not always for cheap though, but you can find cheaper ones on eBay/ Aliexpress that are good enough.
From experience, depending on the complexity of your circuit, it can actually take up more of your time hand wiring all that compared to designing a PCB and have it made for cheap, so most of the time, in my case the prototyping on such boards is limited to small circuits / evaluating some specific IC / etc.
What do you do if you need higher-density packages?
Depends. Either I can use dedicated (small PCBs) adapters with the required footprint, or I sometimes hand-solder tiny wires on the IC pads (very rare, but I have on occasion).
I tend to favor using ready-made breakout boards or evaluation boards though, if available for a reasonable price. A time saver. So I usually look that up first.
(b) What is your personal "sweet spot" size for passive? 0603, 0805? I would want to order E12 or E24 sets of resistors and capacitors, but only in a single mechanical size.
Depends. For proto boards, 0603, 0805 (or larger if required by power dissipation considerations). Anything smaller than 0603 for all-purpose SMD proto boards is a bit nasty.
For regular PCBs, there is no sweet spot, it will all depend on size requirements. But I'd say 0603 most often usually. 0402 or smaller if needed. Larger if needed.
(c) I think I have the soldering under control, either pad by pad or using extra flux and dragging the tip. Haven't experimented with solder paste and oven/pan soldering yet, but that would be used for small series rather than early prototyping, right?
Also depends, mostly on your habits, available equipment and obviously, components themselves. If a board can be soldered with an iron and/or hot air only, I will do that for the first prototype(s).
Now if you have to deal with a lot of components and/or more than a couple BGAs or QFNs, using an oven or pan is worth it.
(d) Any other advice for SMD prototyping? Many thanks in advance for your help!
A good soldering iron. Lots of flux in various forms: having flux pens, liquid flux and gel flux is all handy. A hot air station. Decent solder wire.
And lastly and again, do not shy away from designing proper PCBs and having them manufactured. That's quite cheap and fast these days, and unless you are in a big hurry, you'll have a better time overall.