Some good tips on here, not sure about buying a second hand bike unless its one that has been bought and not really used. I have 4 bikes now, two off road one hybrid (also a boardman, halfords finest) and one road bike. Started with a budget bike and the spend has got progressively higher. I have bikes that look like brand new but have done 5,000 miles, they do wear out and repairs can be expensive.
Off road is more fun , possibly harder and probably safer as you dont have to worry about the traffic killing you . You will need a mountain bike for off road , there are lots of different types but I would spend maybe 3 or 4 hundred pounds on a middle of the road decent make.
Road cycling , you need a road bike (no shit sherlock) half decent bike around £1000
Half way house is a hybrid which would let you do a bit of road and enjoy the many cycle paths in South Wales. Taff Trail is a brilliant way of spending a sunny afternoon. Probably best place to start, no cars just people with dogs and kids to manoeuvre round.
Get a cycle helmet, padded shorts put a gel seat on your saddle for extra protection.
Take your time dont try to kill yourself knocking up miles
Get the map your ride app and you can monitor the miles you covered and the difficulty in the miles.
I started cycling round your age( a few years ago)
. I am about two stone lighter now, have done cycling holidays in the far east , doing Mallorca with my partner in June . Possibly as fit as I have ever been.