Yes those Mega328 testers work well.
I'd skip the large combo kits, like avionic said you won't use most of it, and the other thing is the parts may be of questionable quality. I think it's worth taking your time and making a list of all parts you need, then just doing one large mouser order (and getting free shipping) instead of many small ones. With mouser / digikey you're guaranteed genuine parts, worth paying a little extra for in my book.
FYI it's fairly unlikely for ceramic and film caps to blow anyway. Usually most failures will involve a combo of semiconductors (transistors, diodes, etc) and resistors. If you do the thing I suggested where you mark in red the failed parts on the schematic, we can help suggest some surrounding parts to test (so you don't have to test / replace more things than you need to).
It's probably good to wait for the Mega328 to arrive, and also I wouldn't recap it until you get the problem fixed - but if you do - just be careful to note polarity of what comes out (use a marker to mark negative on the board before removing the old caps, perhaps).