Since Lightroom and Photoshop (at least in its current form) is still heavily biased towards single core performance, you may not benefit from the added multi-core performance of the i5 and i7 version; I think you will be more than fine. 16Gb is a good base ram to have. You probably won't need to upgrade ram after that unless you are working with 36MP and up files with layering. If you are only dealing with 16MP to 20MP files with modest layering, then even 8Gb is fine. Photoshop does not utilize the GPU performance all that much -- only a few features use them so even the basic iGPU is fine. You do need to use an external USB 3 drive for storing all your photos though and to remove any bottleneck if you have lots of photos to curate in lightroom is to get a Thunderbolt 3 chassis and run your drives in RAID mode. Lightroom is more of an I/O sucker than a CPU sucker.
In terms of buying a monitor. This is when I will say to you that it's actually more cost effective to buy an iMac 4K or 5K with the same i3 Mac Mini spec, because the monitor itself is very nice, color balanced and sharp. To get the exact external monitor as the iMac with the i3 Mac Mini would actually cost you more. Basically, the best way to get a Mac with a nice monitor is to order an iMac with 16Gb RAM and either a fusion or SSD drive. Then get an external drive as your photo storage drive and scratch drive and leave the boot drive as your application and VM drive. This setup will speed up Photoshop and Lightroom immensely rather than trying to brute force Photoshop through buying a faster CPU and doing everything on just 1 drive.
I use Photoshop with my old 2011 Mac Mini and it is still fine with it because I have a SSD for my boot drive, a fast SSD for my Photoshop scratch drive, a fast RAID 5 photo storage drive. The only thing that's slowing Photoshop down is my single core performance on the Mini is slower than the i3 Mini when doing layers and plug-ins. My sister is running with a 2014 Mac Mini i5 1.4Ghz and she's doing just fine with Photoshop as well working on her art projects. The key to Photoshop speed is good drive management and then single core CPU speed.