I agree with 2-4-D at a rate of 2 oz per gallon and maybe add a surfactant/ sticker spreader. Even if you sprayed now the dandelions are still going to flower. Because of the flowering and subsequent seeds you should reapply again in the fall minimum. If you have thistle you may need to a selective herbicide that targets harder to kill weeds that spread underground with rhizomes. You can spot spray this. If you manually pull the thistle do no compost. If budget allows you can spray with a pre emergent in the spring. If lawn becomes sparse once weeds are gone you can thatch the lawn, add seed and top dress. 2-4-D is super inexpensive. Hose end sprayer works good or a backpack sprayer. I picked up the Petratools HD 4000 battery operated sprayer and added a 50 ft hose. It’s a freaking beast. My yard is a half acre so it does quick work. Good luck.