Do you know the width of the rear stays/ axle? If its 130mm you may have trouble running 8spd wheels as the last cog may catch on the rear stay just above the rear mech.
I would strip and clean the frame, purchase the triple chainset, new front and rear mechs plus a set of road specific flat bar shifters/ levers. These then allow the use of the existing brakes and wheels.
If the frame is 'close clearance', tyre choice will be limited as anything too wide will hit the front mech and/or the stays.
If the original wheels are 'cassette' - a new wider range 7spd cassette is readily available.
I dont know your budget but the following are suitable for the build:
Cassette: http://www.ebay.co.uk/itm/SHIMANO-7-SPE ... 337ca7fe0fhttp://www.ebay.co.uk/itm/SUNRACE-7-spe ... 46071b16d1
These are bomb proof and are suitable for your road brakes - http://www.ebay.co.uk/itm/EZI-FIRE-SHIM ... 35bf52cbb4
'Proper' flat bar type road shifters: http://www.ebay.co.uk/itm/Shimano-Sora- ... 4846eb8bbf
'Budget' - http://www.ebay.co.uk/itm/SR-SUNTOUR-XR ... 43b9bfae65
'Bargain' - http://www.ebay.co.uk/itm/New-Shimano-A ... 1e76aab3df
'Quaility' - http://www.ebay.co.uk/itm/Shimano-Deore ... 1c3130ffb5
Chainset (dont forget to change the BB!)
'Budget' - http://www.ebay.co.uk/itm/triple-mtb-bl ... 1c31586c15
'Bargain' - http://www.ebay.co.uk/itm/NEW-SHIMANO-F ... 484f41e147
'Reasonable' - http://www.ebay.co.uk/itm/Shimano-2300- ... 4847003868
Then theres front mechs and you'll also need these little fellas - http://www.ebay.co.uk/itm/Shimano-SM-CS ... 43b035dfb6
to replace the downtube shifters
You can also re-use the downtube shifters with a set of these: http://www.ebay.co.uk/itm/Velo-Orange-T ... 2ec6f0637f
The list of available parts is endless! Thats just new stuff, there an almost endless supply of retro, second hand and so-on...