However, from what you say the case isn't the best option - I realise this site has case recommendations (which I've started reading), but what case/PSU would you recommend for someone with my planned build. Ideally the case would be less than 14 inches tall to fit under my desk drawers, but if that'd require too many other compromises it can be taller. Ideally I'd spend under £100, though I could stretch to under £200 if there was a really compelling case (so to speak
I have the NSK3480 and I like it very much: but it isn't a fire and forget option, you have to work onto it (modding: first of all, you have to mandatorily swap the exhaust fan, the Antec TriCool is horrible, according to me).
Moreover, it isn't the one I would advice for a novice, I would stress upon that it's very uncomfortable working inside it.
However, if you want to fit it under the drawers, it isn't recommended: this case needs a bit of air around it to breathe effectively, and it has a top intake for the PSU.
Please take note that AFAIK there isn't any mATX minitower which is less tall: there are some big cubes like some Lian-Li V-series but they are expensive, and a bit too flimsy (they lean towards resonating).
The EarthWatts PSU is really noisier than any recent Mac. I have modded mine with the R8 about two years ago and I've never regret of: running the fan with a mobo header at around 3-400rpm, 700rpm under load, it's one of the quietest PSU I've ever heard (and I have several ones, including a four years old fanless FSP Zen).
If I were looking for a compact chassis, probably I would look for a Silverstone TJ08-E or an Antec Solo II.
Both are a bit taller than the NSK3480 and fairly more expensive.
Personally I would look even at the Lian Li PC-A05 but it needs some mods (mostly padding).
Some proven but bigger alternatives are the nowadays classical Fractal Design Define R3, and the slightly more little Defini Mini.
They are less sturdy than a Solo, and more than SS or LL, but they are more easily workable and with a probably better quality/price ratio.
NZXT H2 is also appreciated, but it is less refined tha FD ones, and in Europe goes for about the same money, so to me it isn't preferable.
Probably the last workable options - I would consider - could be some steel-made Lian-Li, the Lancool K-5X (7/8/9), and the Cooler Master Silencio 550.
They are a bit cheaper than the other already quoted enclosures and you may like the design. Read the relevant SPCR reviews about them, if in case.
Open (gaming) case, such as Antec Hundreds-series or Fractal Arc-series, are more challenging options, due to their vented front bezel, so I would avoid such a solution for a novice.
To stay on low as total expense, I would couple them with something like a be quiet! Pure Power CM 430W (L8-CM-430W/BN180) or, if you may rather an SPCR recommended unit, an Enermax LibertyECO II 400W (ELT400AWT-ECO II). Nexus Value 430 is also a good (see charts) option (even if it has a cheap construction and there are some reported quality issues about it), and there are several good reports about the Cooler Master Silent Pro M500 (RS-500-AMBA-D3), which's big brother is well recorded in the above charts.
I think that such a combo would start for around 130£ shipped.
You may save something using less refined/known enclosures, if in case. I'm testing the NZXT Source right now: it isn't that bad, and it will leads you around 100£ for the combo.