You see, neither of us wants to be continually fixing or upgrading stuff. We'd rather her machine was running on traditional lines if it's likely to be more reliable. You see where I'm coming from?
My recommendation is to start with the size of the case and work sideways from there.
I would consider a case designed to fit a micro ATX motherboard to be the largest you'd want for your needs. Something this size has sufficient space for bigger fans to keep everything whisper quiet (or silent, depending on your requirements) You'll have space for a DVD drive if you require one and if you do need to add a hard drive or upgrade the memory, you've got the space to move about.
Smaller cases are available, from slimline units about the size of a games console to tiny book sized units that are small enough to bolt onto the back of the display.
You may find that by specifying a smaller case, the price level goes upwards, smaller always being more expensive. You'll also find that when you look at full sized units (To me this is Micro ATX rather than some kind of monster tower the size of a suitcase) they tend to be specified for the gamer market and specify expensive components and lots of lights, clear case sides and that sort of tat the grown ups don't want.
£400 is a bit of a push for a complete build done properly. The £ to $ exchange rate has taken us back to the good old days, where a dollar is equal to a pound and prices reflect this. I know you're not planning to build the machine, but Windows 10 costs a big chunk of your budget, so someones going to have to pay for it.
What you might be looking at as a minimum specification could start with:
Processor - AMD do a quirky little unit - The 3400G. Odd little chip, quite a quick quad core(Boosts to 4.2GHz) with SMT (one core can act as two some of the time. Intel call it hyperthreading) It has on chip graphics which are relatively powerful (will help with photoshop) £139 mind you.
Dual core processors became too slow a couple of years ago and some of the i3 range (dual core with hyperthreading) don't really keep up to well anymore. Intels numbering conventions have become so bizarre it is a stuggle to keep up with them. They sell both dual and quad core chips as i3s and then you've got to work out the generation. You'll get better value from AMD, but the key to me is seeing that 4.0GHz or higher clock speed and at the very least quad core.
Memory is easy, you'll want 16GB, for a budget machine with no independent graphics card, faster memory does help but as you're not gaming it won't make enough of a difference to be concerned about.
Assume about £60 for memory.
Some of these pre-built computer sellers, use some obsolete components to get to a price point, they also cut a few corners in spec and hope for the best. Of particular note is using conventional hard drives rather than SSD drives, even if they offer an SSD, they would be likely to use the latest generation of not very good, but very cheap SSD drives.
What looks like a half decent 1TB SSD is going to be in the region of £90. This requires research, so see what the drive actually is, or failing that, get something with a hard drive and buy your own SSD.
A decent motherboard will have a newish version of USB (now apparently at version 3.2), I wouldn't panic too much about this, I would panic if they offered such a cheap board it only had USB2.
Essentially, if a company does not specify every single component by brand name and part number, don't bother with them.
You might get better value from one of those companies who build a machine to your exact specifications, it's more work at your end, but to close this off it's worth considering cars.
A car is an amalgam of it's own performance, a mid sized car has a certain engine which is matched to the brakes and tyre size for optimal performance.
A youngsters performance car does some tricks to the engine, puts on the biggest wheels that will fit and forgets the brakes are not up to the task.
A mid range PC should be the Ford Escort of cars, an excellent blend of components each working optimally.
The stuff they sell on well known sites makes me shudder, top of the range processor from a few generations back, coupled with a shonky power supply that is unlikely to last a year unlikely to deliver its massive quote power output. Kids computers.
HTH,
I'd up that budget to £600 if possible,
B.