Villager:

 

 However, the main problem is speed. Sometimes it seems when I type, it takes a while for the cursor to catch up.

 

 

You existing PC has serious issues .
Even a low low spec 10 year old PC shouldnt lag just typing.
Fixing you existing PC may be a cheaper option , if you cant afford to replace it.

 

"may have a dozen windows open on two displays."
you want lots of RAM

 

i3, 16Gb RAM, 500GB SSD, Win10 Home
Start there . Or Ryzen Equivalent (prebuilt).
Start with a good sized SSD , not something that allways going to be running out of free space (eg 256 Gb)
Dont be suckered into a PC with a small 256Gb SSD &  1Tb  old school HD.

 

 

 

Basicly , you need to spend as much as you can afford .
More $$ = better user experience .
Consider everything in your current PC obsolete & in need of replacing.
Dont going trying to upgrade old hardware or buy bits from various suppliers ...unless you REALLY know what youre doing . Are you going to do bios upgrades on mb if it doesnt support(as is) the CPU you buy. Thats happening to some .
:-)