In fact the majority of flowering plants do - grasses and most trees are wind-pollinated. Most of the plants commonly pollinated by insects are also capable of self-pollination. That is, they can breed with themselves, within the same flower. There are of course exceptions to that (fruit trees generally require insects, for instance) but for the most part, plants would go just fine without pollinating bugs.
So why evolve towards that direction? Because insect delivery is more efficient. A wind-blown breeder has a perfectly random chance of passing its genes on through pollen. Insect-born pollen is delivered much more certainly. Those plants whose flowers attracted insects thus simply had a higher rate of reproduction, and the insect-attracting genes were the ones to spread. Plants that delivered the most pollen to the most insects and did so in an efficient manner - such as those plants that react to the bee by whacking it in the head with a wad of pollen - would also have hteir genes spread better.
As for whether plants or animals evolved first... Depends on where you start counting them as "plants" and "animals"
