As someone who has been using Lightroom for five years I have the following input:
Clock speed trumps cores. Extra cores improve performance when exporting images but that's about it - everything else is mostly single threaded. Unless she is going to be exporting 500+ images on a regular basis, even a Core i3 will do for most tasks if you could get the clock speeds high enough.
Lightroom eats RAM for breakfast and performs like a dog when it runs out of free memory. It's a situation where a slower hard drive with more RAM beats an SSD with more less RAM. You work on one image at a time, which will be a few dozen megs at best (assuming raw files and not JPG, which are even smaller) which is about well under 500ms of sequential reading even on a slow drive. Once it's loaded to RAM, that is where it resides and with RAM bandwidth in the 10s of GB/s not even RAID0 NVMe SSDs can compete. Have a look here and you'll see that even slow hard drives with speeds of up to 150 MB/s can keep up with NVMe drives with speeds exceeding 3,000 MB/s
Adobe Lightroom 2015.8 Storage Performance Analysis
A graphics card is a waste of time unless you have a massive budget and have maxed out most of the other specs. Very little is GPU accelerated, and there are a lot of issues. Frequent issues include extreme lag when swapping between images, intolerable lag when using the brush tool, image blacking out during certain operations, etc. I leave it disabled. For the most part, a Titan V (which is a $ 3,000 card) is only a few percent faster than integrated graphics
Photoshop CC 2018 NVIDIA GeForce GPU Performance
When it comes to Photoshop, which I've been using for about as long, most of the above is true but I'd take an SSD over more RAM.
For your budget I'd look at something such as:
Core i5-4670K/Core i7-4770K/Core i7-4790K
- A Core i3 is not recommended as they have a much lower clock speed, and jumping to a 6th gen CPU is a large price increase for a not so large performance increase
Any LGA1150 motherboard
- Seriously, you're getting this for Lightroom on a budget. Go H81 if you have to
16 GB DDR3-1600 or, better yet, DDR3-2400 if the price isn't too high
- 8 GB just isn't enough unless the budget doesn't allow, and 32 GB is overkill. 16 GB is the sweet spot
Integrated graphics
- It's more than adequate unless you have spare money for a graphics card, in which case spend it on a faster CPU instead
120 GB SSD for OS and Lightroom/Photoshop installation
- Booting and launching apps from a mechanical drive is painful
1-2 TB HDD for storage
- Unless you're like me and have a problem with deleting, you probably only keep one out of every few dozen shots. When I was shooting film I'd consider it a decent day if there was more than one photo worth printing. You'll wear out your shutter several times over before you have 1 TB of "keep" photos even in raw format. I have an issue with deleting anything, but if you were to hold a gun to my head and tell me to get over it there are around 500 MB of photos I'd keep of the +/- 3 TB I've got
External drive for backing up (VERY IMPORTANT)
- Drives die. Your photos don't have to. It's worth considering cheap cloud storage for the really great shots. 3-2-1. Three copies. Two mediums. One off-site
Cheapest case you can find
- This money is way better spent elsewhere. Grab an old "gaming" case from the mid 2000s if you have to. You know those ones that used to sell at your local computer shop for R 250 including a no name brand PSU? Yes, one of those. Just chuck the PSU as it's likely a fire hazard and you can't afford for a piece of rubbish to be taking out components that are already well out of warranty.
Corsair 450w PSU or similar
- If you hit 150w power draw I'd be surprised.
Once you're running a Core i9-9900K with 32 GB RAM we can start looking at a graphics card, but all I ever see mine doing is playing Solitaire in the background (or Minesweeper, I don't know what graphics cards do) while I'm busy with photo editing.
This is not true of the entire Adobe suite, nor is it entirely accurate when doing more than just a bit of hobby photo retouching in Photoshop (if you start doing a lot of blurs, perspective warps etc the GPU gives a nice-ish boost, but those aren't generally things used with photo editing), but given the applications and use case at hand it's about the best you can do.