Doing the GPU first would be interesting and help give you an idea which games need the CPU grunt more than the others.
If you're wanting to save some dosh, you could just postpone the troublesome games till a later date, though I know that would be disappointing with a new shiny to play with.
If you're planning to upgrade the monitor (higher res) then I'd go with a 9070 or 5070, at least, especially for 4K.
Be wary of large core count CPUs. I don't know much about your socket, but large core counts tend to boost lower and when you have a dated CPU you'll need all the clock speed you can get. More than 6 cores is in diminishing returns territory for the majority of games.