There's a significant price jump from 2K to 4K so I would recommend not getting a 4K monitor unless you specifically intend to edit 4K video.

Since eyesight is your problem there is something to be said for going large. 24" would be a jump up from what you have but 27" would be even better and the price difference won't be that big. You are right in thinking that you don't need a pro level monitor.

With a higher resolution screen, the size of the text will be reduced but you can increase it by adjusting "Scale" in Settings. You can also adjust the size of the pointers and cursors.

You should leave the computer to use the native resolution of the monitor (it should do that by default).

Here's a review / product description of Luminar AI:

https://www.photographyblog.com/reviews/luminar_ai_review

I have no experience with the software, having not even downloaded the trial version. Based on the above write-up, the advice you received to start in DPP is invalid, and instead, you should just work entirely within Luminar AI. As you advance in 21st century digital photography, you're going to many times encounter the fact that some 'rules' are nothing but old habits that people are afraid to change.

Speaking about Adobe, and by extension other RAW editors, an important action / change to make is to find and use the 'camera profiles' and 'lens profiles' of the third-party software. So in Canon DPP, or Nikon Capture NX-D, these softwares default to the camera's 'standard' profile for saturation and sharpening, creating RAW images that look like the camera's JPEGs. Adobe instead uses something they call 'Adobe Standard' that is much less 'rich' in terms of color. But, in Adobe Camera Raw and Lightroom, you can change this import default to 'camera standard' and suddenly, your images will look like the camera's images as the start-point for your editing.

When you become a RAW photographer, you become the decision maker for these considerations in post processing, where many had been decided by the camera for the JPEG:

1. Sharpening
2. Noise Reduction
3. Color Saturation
4. Exposure adjustments, general
5. Contrast, general
6. Highlights and shadows
7. White Balance
8. Lens corrections
9. Color space
10. Pixel resolution for target image share platforms
11. Disk storage (for the larger files)
12. Image file back-up strategy (for those larger files)

You don't have to understand all these issues, but when you do, you'll be much more successful as a RAW photographer. Reading about Luminar AI, maybe some of these items are now being handled by the AI software? You might take each topic of 1 - 10 and investigate the topic and them how / if that topic is handled by Luminar AI, or whether (and how) you still need to add your own Human Intelligence to the RAW processing.