I just use one VOM and start up in stages, checking for expected voltages as I go. The procedure may vary slightly depending on the circuit, But basically before putting tubes in, I turn it on and check for proper PT voltages and watch/listen for boogers. I verify the bias supply if applicable. Then I check for proper filament voltage at all tube sockets by probing the tube side of the sockets. Then I enable the power supply and check for voltages all the way down the rail. Next probe the socket plate/screen pins for B+ and grids for negative bias if applicable (again from the tube side). I will set the negative bias to maximum if adjustable. I'm not looking for correct voltage at this point (still no tubes plugged in except maybe rectifier), but the presence of high B+ tells me that the plates are probably wired correctly. Then I pop in the little tubes and check for proper plate, grid, and cathode voltages (again knowing the plates will be high because no power tubes are plugged in yet). And finally I plug in the power tubes, monitoring cathode voltage/current. Hopefully it's time to plug in the guitar and watch/listen for surprises.
And don't forget your best monitors are on your face. I'm constantly looking, listening, and smelling for abnormal signs throughout the entire startup process.