Most climbers (and shrubs) will require a large pot, it will have to be about 2' wide and the same high.
Pots smaller than that won't allow for root growth and your plants will eventually die off - wasting your hard-earned cash.

So, i would buy a number of pots that are that size and position them around your pergola so you can see where you want to position them, then google these plants and see what you fancy ......

Evergreen climbers .....
Ivy (fast growing, flowers and berries, self clinging)
Some Clematis (fast growing, flowers and afterwards seedheads, self 'twining' (not clinging) to THIN wire - won't cling to anything larger than 1cm )
Some Lonicera (fast growing, flowers, not self clinging or twining, needs tie-ing in)
Hydrangea petiolaris (slow to start but fast after, flowers, self clinging)

You could grow deciduous climbers aswell and they'll climb alongside the evergreen ones but i've concentrated on the question you've asked and not added deciduous here.

We could give a more definite, and possibly longer list, if we knew about where you lived. So much depends on climate!