Ok, well the bike that you've picked is a pretty basic off roader. Gears will be suited to climbing and as you can see it's got off road tyres. Off road tyres on the road can be a bit dodgy on tarmac in the wet at speed, not to mention it's hugely inefficient since the rolling resistance is significantly higher than a road tyre. Of course, if you're training for fitness, this isn't really an issue in my eyes - I commute on an offroad bike with off road tyres and whilst it does slow me down, I enjoy having to work that bit harder.
If road stuff really is your thing then you're looking at either a full on road style bike or a 'city' bike which is kinda inbetween a road bike and an MTB. £300 will get you a pretty basic bike in either form but personally I'd be leaning towards an urban bike rather than a road bike. Personally I prefer straight bars and there's also the road condition aspect - around where I live a full on road bike wouldn't last 5 mins, and you'd be forever getting the wheels straightened!
Funnily enough I was looking at a £300 urban bike the other day. Probably not suited to you since it's a single speed (no gears!) but I just love the look of it!
Charge's Plug
http://www.bikeradar.com/gear/catego.../plug-07-20542