Just a power amp, turntable and speakers?

unless you are mistaking a power amp for a receiver.Then your phono preamp,volume and tuner are all included.20+ years ago.

get a vintage marantz integrated amp....plug your table in.....you are home free.

I actually just got an HH Scott 436 integrated unit, but it seems like it's a little underpowered for the speakers I'm running. I was just wondering if I could employ just a Crown or Marantz power amp alone, and take the Scott out of the picture since the turntable is the only input. (I only have experience with modern integrated receivers)

Any suggestions on an appropriate power amp to pair with the Scott 436? Is there a reason to avoid a late model Crown? Or should I go with something more age appropriate?

As has been said, you need a volume control in the circuit, which is what a preamp does. Otherwise it would simply play at full volume all the time. Plus you must have a phono preamp, either built in to the system preamp, or a separate unit. The phono signal is very low output, plus it is equalized with an RIAA curve, and sounds horrible without the proper re-equalization.
Does your Scott integrated have pre-amp output jacks on the back? If it doesnt, you cant add a separate power amp to it.

Yes, the Scott unit does have a pre-out.