Is there a slightly stiff link in the chain from installation? The wrong sized chain shouldn't make it skip unless it is inadequately tensioned by the derailleur. If the chain is tensioned in the small-small combination you should be OK there. To check for excess wear on the chainrings, look for sloppiness of chain around chainring, or chain not seating firmly to the bottom of the teeth.
Oil is good, grease is better.
2007 Peter Mooney w/S&S couplers/Terry Butterfly
1993 Bridgestone MB-3/Avocet O2 Air 40W
1980 Columbus Frame with 1970 Campy parts
1954 Raleigh 3-speed/Brooks B72