Have a look at my build log a couple years back. I don’t know what you have in mind as far as system requirements, but your $2500 USD budget is going to give you a lot of options.
Do you want a descrete GPU? That makes it more challenging, but will reap major rewards.
It’s really tough to make a recommendation without any clear requirements other than portable.
Ohhhhh, ok. My recommendation then? You’ll want a good (not top of the line, but good) CPU. Certain emulators are surprisingly CPU intensive and require some pretty decent single-core clocks to maintain. Maybe this isn’t so much the case these days, but back in the day, Dolphin was pretty tough to run.
I’d grab a 7600 (or 7600x), 16-32gb of ram, or whatever you have on hand, throw in a couple of those 905p’s you have laying around and call it a day.
Or, find a mini PC with a 7600/x in there and enjoy that, for probably less money than you’d spend on a custom build.