I'd realy recommend trying to jump up to programmable logic. Better if you learn VHDL (of verilog) and then creating heavy logic becomes a pure joy and art.
You can make your own programmer, consisting of only a logic buffer (i can send you a schematic) for LPT (printer) port and software is completely free, if you choose Xilinx parts, for example a CPLD: XC9572XL (that is now becoming obsolete, but still rocks) that costs a few bucks in a reasonable package (VQ64). FPGAs are also very very cheap. Development kits can be found starting from about 50bucks. Other vendors (lattice, actel and altera) could also be tried out, bet there are many crappy things I came across, such as written NDA agreement to be signed and negotiated with Actel, hidden tricks in even lpt programmer to limit software quality (hidden jumper that is missing in publicly available programmer schematics, when it is not present software behaves poorly - forcing you buy the official programmer), and so on...
I recommend xilinx just because I have used it for about 10 years in hardcore highspeed systems and it rocked. Actel also rocks.
You can download a lot of unofficial hardware available, including the PSG chip (!) and various peripherals (
www.opencores.org) if you use programmable logic (of whatever vendor).
Here's a nice guidebook into programmable logic, just skip the xilinx marketing blahblah:
www.dtech.lv/sega_dev/logic_handbook.pdf
However - if you choose the hellish 74-logic path:
Paula made in 74 logic will not be so simple

It will be quite hardcore, realy. In old russian drummachine designs, where they did not have any similar asics (like roland, korg and yamaha did), dsps and signal processing knowledge, they used two current multiplying DACs in series. The first one generated volume as a current reference for the next one, which played samples from directly connected roms. I'd recommend perform shiftdowns for programmed amount, using downcounter with programmable load. Volume att. step would be 6dB, which is very coarse, but you need multiplicaion to make it more fine. Technically it would work by having 16 cycles for calculation and in the inital cycle load up 16bit shift register with sample and downcounter with the att. value. 16bit shift register shifting right occures while downcounter is not at zero. downcounter count down also executed while caounter is not at zero. result is read out of the shift register.
If you want to make dac, you can make your own PWM, but don't expect it to be any further than 10bits. Remember that you need samplerate*(2^bitwidth) cycles speed for such output system. Meaning that 32kHz output will require 32.768MHz clock for all this machinery. If you'd use sigma modulation techniques (synthesize DSD stream), than 2Mbit/s would be enough, but logic board for one channel will then take size of a snow shovel.
I'd remind that running it faster than a few megahertz is highly unlikely unless you can make a high quality PCB with short and length controlled traces instead of breadbording with wires.
I would recommend using a ready dac with one of the standard serial interfaces that has LRCK BICK DIN pins (as an example), and drive them serialy. You can even extract such DAC-s from some oldschool CDROMs and many old CD players. All you will need is clean +5V supply and dual opamp after it (can also be extracted from the same machines).
Using pure logic also makes burden due to specific bitwidths and gate counts per chip, so that you will frequently bump into bitwidths not fitting into logic, and if you add some logic, there's too many free, and if you borrow a gate from another chip and kind-of simulate the missing one, you find the timing got severly skewed.
Regarding VDP, creating anything more complicated than CGA or ZxSpectrum video sequencer, is quite impossible on discrete logic, too. Largest and the most hardcore video board that I've seen, that's built on logic was "olivetti" - kind of CGA with some extended video modes and video memory, that was full depth ISA card (kind of ~40cm by full height) filled with DIP chips.