As costs come down and technology progresses - you can indeed buy a really decent mountain bike or hybrid -
new for as "little" as £400. As ed says - these were a lot more expensive 10 years ago. You can of course get something more "up market" second hand - but I think my wife's suggestions would fit the bill for a returner to cycling who wants to ride as you describe.
Both Diamondback and Ridgeback offer a good range in the £400-£650 range of their bikes... and the Comet is a really nice model. Another reccomendation from asking across this family would be a Marin Stinson - or Larkspur - both aluminium frames and light to ride.
Giant and Trek also offer a similar mid-range of hybrids.
All of these are acclaimed precision manufacturers. As johnsher says - essential to get the right size and set up for your height and build. You have to feel comfy after all.
I would visit a few bike retailers - including Halfords (but avoid supermarkets
) Sit on them. Test ride them. Customise the saddle.. try different ones. Gel ones are comfy
Helmets? Most are made to British standard - and there is no difference in real terms between a budget one and an expensive one - other than style, colour and fashion
I would say sun glasses (and I prefer ordinary reactolite sunspecs to overpriced ones sold at bike shops
) are a must as are gloves, lights, lycra leggings or shorts. Or if you do not want lycra - any sports gear will suffice and I stress to dress to be seen easily.
Bikes are narrow - and we need to make ourselves appear just that bit more larger than life to some of the numpties out there