Hi Coykiesaol, Jasminum nudiflorum will be a total waste of time, its not vigorous enough and will take ages to cover (if at all) I think I would opt for somthing thats vigorous and or evergreen ! You havent said where you live but these may be useful options. Polygonum baldschuanicum (Russain vine) very fast growing, a good covering climber, whilst not evergreen, it will be your cheapest option. Passiflora caerulea (passion flower) again not evergreen but a very fast, covering climber. Clematis montana, again very fast growing but not evergreen.
More expensive but evergreen would be Hydrangea seemanii, slower at first maybe but dense when established. Lonicera Halliana (evergreen honeysuckle) quick growing semi-evergreen climber.
Dont worry about climbers that are vigorous, work on the basis that its better to have the quick cover, you can always trim them back if needed !
Also dont be afraid to plant several of the above and let them grow together, that way, youll get the benefit if the flowers at different times of the season, from what you say, cover and privacy is the most important.
Plant any of the first group at 6ft apart (approx) most, as I say are very vigorous.
Hope some of this helps, Lannerman