An obvious upgrade from the 16F627 would be something like a 16F877, and an upgrade from that an 18F series - but if you wanted to jump direct to the
18F series that would be fine as well.
If you want to stay with the 16 series then I would suggest the 16F886 (28 pin) or 887 (40 pin) as these have an internal oscillator whereas the 876 and 877 don't.