What colours do you like? White or pastels or oranges or purples and blues? There are climbers for every shade. I really like Clematis montana 'Marjorie' at the moment: it is vigorous and a subtle shade of pink and cream with hints of green and a pleasant scent. Montana 'Broughton star' has a very pretty deeper pink flower. Honeysuckle smells irresistible, and comes in many colours from white through to bright orange and purple. The vigorous viticella clematis flower in late summer and come in the deeper colours. Climbing roses are lovely to have, and my favourite is the white and vigorous Alfred Carriere, which flowers in midsummer, but there are gorgeous pink climbers and deep maroon climbers, and orange climbers such as Mrs Oakley Fisher, which has a lovely orange open flower and delicious scent. As they mature they take up space, so it is nice not to plant too many. Choose wisely.
You can plant them now if you like. I would avoid wisteria on a 6' fence panel as it will outgrow it pdq; clematis montana would too but you can hack that back if you need to. Any clematis would be nice, you could have an early one and a late one so you spread the flowering. Ditto a small climbing rose - some ramblers get absolutely huge. David Austin catalogue is good for sizes and places for roses.
The clematis and some roses will do well on the south east side; the honeysuckle may be happy on the shady side and some roses will be happy there too - again check the catalogue. Sweet peas on the south side would be lovely.