High speed counter for digital oscilloscope
What you want to do is possible (just barely) with 74xx ICs, as long as you don't need excessive trigger logic complexity, and as long as "xx" means something other than 7400 series.

The 74FCT family will give you counters and registers up to about 100 MHz, so that's no problem. The hard part will be digital triggering. By this, I mean that you continually run the ADC, and examine the digital output to determine trigger status. Your best bet would be to use 74F85s in a pipeline configuration, and theoretically you can get about 40 MHz for 8 bits. 12 bits would be harder, but I suspect you could get tricky and get it to work.

Using a RAM, you need to produce a 40 MHz counter to determine acquisition window, so using a FIFO will be a big win in complexity as long as you want a data window which is the same size as the FIFO, since you can play with the FIFO full/FIFO empty flags to control your read and write functions rather than using an external counter to control your read and write bursts. It would have the advantage of decoupling the read and write functions to the RAM/FIFO (no need for address and data multiplexers).