True enough that bulbs don't last as long as bedding - but they do add something a bit spectacular, so maybe a few pots of bulbs amongst some bedding type?
Most summer bulbs and tubers, incl Dahlias you can pot up now. Read the instruction for how deep in the pot they need to go. Again the packet will tell you when they flower, but Dahlias and Lilies typically July/August. Nerines are much later, Oct/Nov.
Spring into Summer you need biennials, which are my absolute favourites. Look out at the garden centre in the next few months for plants of:
Sweet William
Sweet Rocket
Anchusa azurea
Sweet Williams grow well in pots and there are a big variety of pinks and whites as well as mixed ones. They last a long time - appearing sometimes as early as end May and lasting well into July.
In terms of what goes with what, thats so personal, I would just say try to get a mix of stuff that will last you through, so a mix of biennials ( from end May ) , bedding ( eg Laurentia, Verbena, Lobelia etc ) - flowers from end June normally, and summer bulbs and tubers - from July.
If you have some soil to plant in by your trellis, as opposed to a pot, for a scented climber its very hard to beat a rose. The David Austin website has roses to die for. You can plant them up until the end of this month.
If you look for ones that repeat flower.