Quoted:
The title pretty much says it all. Lightroom takes forever to export photos and taxes the whole system. Premier etc. also take forever. What should I be looking for when I buy a new one? I have no idea when it comes to computers as I usually just buy one for about $500 every 8 years or so and it suits me fine. This time I'm willing to spend 800-1K if it's a screaming deal. I'm no pro, but I need something better than what I have now.
View Quote
You need a decent amount of RAM (16 is probably fine, but 32 *might* be better), the fastest Intel CPU you can afford, and if you want GPU acceleration in Premiere, a decent GPU.
Take a look through
this page, even a relatively modest GPU (by todays standards) can cut your rendering time by as 60-80% compared to rendering on the CPU only.
Unfortunately for your pocket book, the tasks you're talking about are some of the few tasks that take every bit of hardware you can throw at them, and leaving you wanting more. For $1k, here are some ballparks...
RAM, $100
Mobo, $120
I7-6700K CPU, $350
480GB SSD, $140
Win 10 OEM, $100
Spend the other $150 on the fastest GPU you can get, going for a used one will take you farther.
I guess I forgot a case, but you can get a perfectly serviceable one for $40.
That will give you an SSD for OS/Apps, a smoking fast CPU for the non-GPU-enabled apps, and a GPU for those that will use it. Move over your bulk storage drive from the old machine, and enjoy. To get significantly faster than that, your costs are going to start going up a LOT faster, for much smaller gains.