Watch out for narrow frames as these only take a 1.9 tyre size. Look for a bike with wide rear forks, you want at least the thickness of your pinkie on each side of the tyre at the bottom and top of the rear frame. Minimum tyre size is 2.10 for off roading, cheap bikes do not always take this size. For a mountain bike secondhand buy two as you can use the forks with suspension and a disc brake on the best frame, [one a non suspension frame, the other a rigid frame, combining the two makes a good mountain bike], the frame has to be the same depth at the forks as it a straight swap. Combining the two should result in a mountain bike with a hardtail, no rear suspension with a decent v-brake, Shimano Acera are cheap and fit a decent cable brake such as the Tektro IO or similar to the front suspension forks plus replace the disk with an Aztec or any decent make. Wheels can be got from woollyhatshop.com Shimano Megarange gears from sjsjcycles.co.uk- derailleurs and freewheels. For a good all round tyre try the Schwalbe Marathon Plus MTB, perfect for older bikes. E-mail me at firstname.lastname@example.org
for more help.