You have a nice set of OLD chips.
I can see no practical use for those chips, you would need probably 20+ chips and a square foot of breadboard to even get close to what a single Mega328 can do, so unless as mentioned you want to make something historical just for the heck of it or as a learning experience I'd move on
As for the Picaxe, it's good for what it is and I've seen many good projects done with it, but there's no upgrade path, when you get more experienced you'll have to learn a stack of new stuff. With Arduino you just add to what you've learned.
I already have an arduino mega i was looking for cheap alternatives so i dont have to buy a whole new board for something that is just used for oscillation(e.g. replacing a 555 + NAND gate that makes a modulated 38khz signal or something that can read the signal).
replacing a 555 + NAND gate