I don't particularly try to achieve a perfect lawn now that I live in the boonies, but I used to.
It takes a couple of years to get to where you want and there isn't a magic pill, especially now that the temps are getting up. Some of those weeds take multiple spraying to kill them.
MSMA will kill off some broadleaf weeds and many weed grasses and it can stun bermuda. 24d kills mainly broadleaf weeds. When the temps get above 80 and mix concentration is high, they both will kill or stun almost every plant....even some that are just nearby. Many commercial sprayers tend to use a lower concentration this time of year because of the risk of (temporarily) killing off someone's lawn by spraying the whole thing. Full concentration should only be used for spot spraying right now with the knowledge you'll have a brown spot for a few weeks.
The seeds for the annual weeds and the roots for the perennials are in your lawn already. Their seeds will blow there from your neighbor's yard and birds and animals will deposit seeds in your yard. They will always come back. All you can do is overwhelm them with constant force.
Starting in October, spread some pre-emergent on your yard. Most of it will wash away over the winter, but do it anyway. All winter and into March when the bermuda is still brown and dormant, spray Roundup (or whatever you like) on anything that is green. In early March, put down pre-emergent again. Now you have to be selective. When something green shows up that isn't bermuda, you'll need to spot spray it with either 24D or MSMA-type product depending on what type of weed it is. I say "MSMA-type" because MSMA isn't supposed to be used residentially now due to the arsenic in it.
Do this for a couple of seasons and you'll be where you want.
....or do like an old neighbor of mine would. He's spread 3x as much 13-13-13 on his yard as he should which would nearly kill off the whole thing in April. By June he had the best-looking lawn on the street.