There is no Mount Snowdon. There is Snowdon.
That aside, you've been utterly misled. A ride cannot be "mostly downhill" unless it starts high and finishes low - you don't mean you're starting at Snowdon summit? I can't for the life of me imagine a bike that'd be suitable for riding down Snowdon on the bridleways up there and also for a further 150 miles. For the first you'd need a MTB with at least front suspension and possibly full bounce; for the latter you want a road bike with slick tyres.
Whatever, once you're off Snowdon it's going to be as much up as down, and some will be steep. Any chance of a route?
'course it's mostly downhill - Snowdon's at the top of the man and Swansea's at the bottom - downhill innit :-)
Pish take aside, to the OP, that'll be pretty hilly and I would get low gears, even though I suspect you're pretty fit. These days 14 speed is likely not a high quality machine. Whilst ideally (controversially) a triple front chainset would be a good thing, given the budget you'll probably not have the choice and will have to get a "compact double" which can have somewhat low gears - 18 or 20. As others have said it's the range that matters, not the numbers. My point pooh-poohing the 14 speed is not that 14 is a low number, but that 14 speed is not (these days) high quality kit. I would get drops - (a) because personally I'd get drop handlebars . for anything, (b) the long distance ride you're doing - drops gives you different positions and gets you out of a head wind (c) you sound like a fit sporty bugger, so will likely do more long distance or semi-competitive stuff for which drops are much better.
Mudguards are very much a good thing, but I suspect you'll struggle a bit to get them at your price point on a "road" bike.
Google "audax bike" - that'd be the ideal thing for what you're about - then see what looks closest to that your price-point - a £500 road bike should be doable, even though you'd have to sacrifice some of the features / quality of the £1500 blingtastic audax bike proper