How much protection is an IC socket?
Even for a beginner, damaging ICs from soldering is not something to worry too much about.  Especially DIP ICs where you will be applying the soldering iron to pin on the bottom side of the board.

A handful of analog ICs are very succeptible to soldering heat. They don't get destroyed, but their performance can be degraded by even normal heat.  Socketing is used when really needed here.

The more common reason to socket is to make ICs field replaceable.  If you blow up an IC or it turns out to be defective (which was much more common in the 70s!) you can just pop it out and replace it rather than scrapping the whole board or trying to desolder it.  Another reason is for ROM chips that might need to be programmed before inserting, or replaced to do a firmware upgrade.  Almost everything now is in-circuit programmable, but that was quite common back in the day.

In any case, if you are set on socketing, there is no problem inserting the ICs as soon as the socket is in place.  You aren't going to overheat a part when soldering its neighbor unless you are doing something really crazy.