Sorted.
Here are the tools that I'll be using and, obviously, this is all highly subjective, YMMV, etc.
Note: I'm Windows 8.1 based so I have no idea how or if any of this applies to Macs or even other versions of Windows.
And, for the record, I'm OS/platform agnostic. If it works for you, I'm happy for you.
Primary Tool(s)
Adobe Lightroom & PhotoShop CC
Yes, despite my previous comments, I succumbed to the monthly deal. We in the UK pay 25% extra but the maths still worked out. More importantly this combination does everything I want quickly and easily. Nothing comes close to Lightroom's speed and v5.x is noticeably faster than v4 on my old Intel Quad Core Q9450 (pre i3/i5/i7).
I'm having to learn what settings work with the D3300's NEFs. Auto in Develop certainly doesn't but the lens corrections and camera calibration do. More playing required.
What finally won me over to CC was the change introduced in LR 5.5 allowing a user with a lapsed CC subscription to still use LR albeit with the Develop & Map modules disabled. For me, and I suspect many others, this removes the 'images held to ransom' objection to Adobe's subscription model.
Secondary Tools
Nikon's ViewNX2
Currently useful solely for viewing focus points as I learn to master the D3300.
FastPicture Viewer Codec Pack
Easy image viewing integrated into my favourite file manager,
XYPlorer. And Windows File Manager if I'm desperate.
FastStone Image Viewer
My wife's tool of choice for selecting images for documents, Facebook, eBay, etc.
I use it sometimes for winkling out dud photos before import into LR.
Rejected - in no particular order.
Sorry about the mixed currency. These were the prices presented automatically to me in my browser.
As only DxO supported D3300 NEFs natively, I used Adobe's DNG Converter to produce a .dng for playing with other packages.
There are, of course, people out there doing great things with all these programs but they simply don't suit me or my needs. Again, if you're happy, I'm happy for you.
ACDSee Pro 7 - $199.99
Clunky, overpriced and offers nothing special though the lens blur effect was fun for a few minutes.
The integration of ACDSee's own cloud storage into the product smacks of desperation to generate revenue rather than the will to develop the program's core functionality.
BreezeBrowser Pro - $69.95
Once a major part of my workflow, it's now both over priced and under developed.
Capture One Pro 7 - $299
I spent more time with this than any of the other programs. On paper (sic) this looks to be a serious LR rival and, to be fair, it starts up pretty quickly and I got some reasonable results playing with older RAW (Canon) files but it was simply too much effort. The interface feels cluttered to me and too many times I found myself leaning forward to see tools and where I was clicking. It sometimes slowed to a crawl when processing possibly due my underpowered machine and crashed a couple of times when building a catalog. The uninstall routine left a few things behind requiring manual removal which fails to impress. Nice online tutorials which neither compensate for the technical failings nor justify the price.
Corel After Shot Pro 2 (formerly Bibble) - £57.99
Given Corel's chequered history and habit of buying and burying / dropping / selling products (PhotoImpact, Bryce, Knockput, KPT Filters) this came as something of a pleasant surprise. Corel actually seem to be developing it. Nothing it does comes close to LR but it is very fast and undemanding on system resources. If you're looking for a program with a reasonable toolset to run on old hardware, this could be useful.
DxO Optics Pro 9 - £79
This was my RAW tool of choice prior to LR so I have something of a soft spot for it. It once did things better than anything else noticeably chromatic aberration removal, noise reduction and body / lens correction. Camera support is added very quickly too. To my eye, LR 5 pretty much matches it now and is considerably faster in doing it. DxO redraws the adjusted preview after each change no matter how minor which quickly becomes annoying. This isn't just my machine either as I've seen some review also mention this.
Serif PhotoPlus 7 - £79.99
I'm a long time Serif user with experience of all their mainstream products though nowadays only DrawPlus remains in my toolkit. Consequently I used a friend's copy of PhotoPlus 7 on his machine (overclocked i5). The image organiser is crude, the RAW engine so-so and camera support is added very, very slowly (the D3200 was eventually included sometime Q1 this year). Factor in Serif's aggressive marketing and the fragmented, unmoderated official support forums and this is best avoided. Pity as PhotopPlus is fun to use.
Right, that's it. Thanks again to everyone for commenting.