What is different between S.E.T/push through amp

For that kind of money, you'll likely be getting a Golden Tube Audio or Dynaco amplifier. Both are good values, but need upgrades to perform best. GTA amps were notoriously poorly built, but the upgrade kits make them sound pretty nice.

Keep in mind that either of these two will give you a taste of how good SET amps can sound. A taste....when and if you go full bore into SET amps, you'll get some pricey stuff (like several thousand dollars) that sounds damn good.

Mechans is correct- read about ultralinear and push pull modes. Both offer advantages and disadvantages. I still have a hard time understanding that gobbledygook. Hence, I just went straight SET.

You will need to adjust your budget in all probability to buy decent Single Ended Triode amplifiers.
Also I don't understand a push through amp. I have been tempted to do that to an amp or two but held myself back LOL. You should read about push pull and uktralinear mode amplification if that is what you were trying to say.