[dtvmcdonald]

That is an electrostatic deflection set: no flyback, instead the oscillator
coil in the third photo. You will need several 6000 volt film caps. Allied Electronics
has them. You may want or need to use larger values than specified (i.e. doubled) for the two 500pF ones filtering the 6kV supply and the two 0.005 uF ones to the vertical
deflection plates. These caps are not cheap. Removing the horizontal output
tube does not kill the 6KV, removing the oscillator tube (12SN7 in the HV box) does.

The picture tube is near-unobtainium. You should put one of those Zener
diode clamper thingies across the filament of the CRT to prevent it overheating
as the other tubes warm up. Use an 8.2 volt one. Other threads on sets
like this, the Emerson 600/610 and the Pilot TV-37, give part numbers at
Digikey or Mouser. Don't test the filament by turning it on! Use an ohmmeter.
If bad, pray and try resoldering the two filament base pins.

Whether to unwrap or just cut and kludge-attach the new part for
replacement caps and resistors is controversial. This is not a rare or super
valuable set (just rare working replacement CRT). Its not worth a careful
capacitor restuff job unless that's your real personal big deal. When
I did my CT-100, which IS rare and super valuable, I didn't restuff since
its not my thing. But I DID save all the old caps so a future owner could.
The harder question is whether to unwrap leads or cut and kludge.

My philosophy is to want to unwrap properly ... BUT to carefully consider
each case. If there are fragile things connected to the lug, or if
the cut and kludge would save having to unsolder parts to get at buried things,
or if there is a risk or burning things up with the soldering iron because
something is buried, I would not hesitate to cut the old part out
however necessary to play safe, even if it meant destroying it. But its up to you.

Desoldering tools ("solder suckers" and that solder wicking braid stuff) are good friends. Old TVs may use other than 60-40 or 63-37 solder that is hard to
get off. In that case you can actually add a bit of modern 63-37 to help along.

If you do do a full unwrap at a given lug, its often good to make sure
resistors are disconnected too so you can measure them with one end disconnected.

I too suggest doing a simple AA5 radio first. ESPECIALLY electrolytic cap restuffing.

Edit: I don't think that inexperience should determine whether to try a pre-1950
magnetic deflection set or an electrostatic one like this one first. They are of
equal difficulty, i.e. nothing special. I would simply suggest not trying an
important (i.e. early color or prewar) set first.