...should I try to go a little bit better than OBS recommends as far as minimum specs?
Yes. A lot better! How much better depends on how much you're going to do before you buy another one anyway.
In 2015, I was tired of working around the limitations of my 2-PC rig - portable laptop and better desktop - and I had used both for far longer than I intended. So I bought the absolute best mobile workstation ("docking laptop", as I called it at the time) that I could. Custom spec'ed out on the manufacturer's website, with the best of everything that would go together, all new. (and expensive!)
I'm still using that hardware today. Does everything I want it to, including two simultaneous instances of OBS and a DAW. I've upgraded the software a few times - it came with a choice of Windows 7 or 8 (definitely 7!), then I upgraded that at the last official moment to Windows 10, always dual-booting with some flavor of Ubuntu Linux the whole time, then switched to single-boot Linux when Win10 refused to update anymore - but the only hardware that I've replaced is the internal SSD because I got nervous about it wearing out and failing unexpectedly. So far it hasn't at all, but I'm using a different one anyway.
So as a data point, this 2015 Dell Precision M6800 runs the current version of OBS just fine at the end of 2023:
Operating System: Ubuntu Studio 22.04
KDE Plasma Version: 5.24.7
KDE Frameworks Version: 5.92.0
Qt Version: 5.15.3
Kernel Version: 5.15.0-89-lowlatency (64-bit)
Graphics Platform: X11
Processors: 8 × Intel® Core™ i7-4940MX CPU @ 3.10GHz
Memory: 31.3 GiB of RAM
Graphics Processor: Quadro K5100M/PCIe/SSE2
It took some tedious trial-and-error on the command-line (because I kept killing the graphical environment) to find the exact one driver that would support both that old (2015) GPU and the modern versions of OBS, but I lucked out and found one. A new GPU won't have that problem.
The most important feature to look for in a GPU, is whether it supports video encoding. That takes a big load off of the CPU, so the CPU can do other things instead. And it doesn't cut into the GPU's performance either, because it's a dedicated part that does nothing else. NVIDIA calls it NVENC, and AMD is lagging behind, so I wouldn't consider them at the time of this writing.
