Don't apply ANY chemical until you do the following (in the order listed):
Dig up a section of lawn that looks brown - in the shape of a one foot x one foot square. Dig no more than 3" deep. Break up the soil under the grass and count any grubs that you find. Run a hand cultivar through the soil under the patch of lawn that you just removed. Count the grubs. If the total number of grubs found is less than 10, you do NOT have a grub problem. I'd probably repeat this test in several different places, but do not apply any grub-killer until you have more than 10 grubs in more then one square of lawn. Also, consider milky spore instead of grubex. The former is natural and won't harm yourself, your children or your pets. It's expensive, but one well-done application lasts for 10 years.
Test your soil to make sure that it's not too acid or basic for a lawn. In most places, your university extension office provides that service and may also tell you what nutrients your lawn is lacking.
Check the shade. Bluegrass only grows well in full sun. Some of your pictures look like you have a mix of bluegrass and probably fescue and also show what appears to be a partially shaded lawn. You'll need to reseed some patches with the correct type of grass seed (see point 7).
Pay someone (or rent the equipment) to dethatch and aerate the lawn.
Fertilize the soil with a good time-release fertilizer. Many people prefer compost, if they can get it. I use a chemical fertilizer because good compost isn't really available where I live. Make sure that the fertilizer you buy contains the nutrients recommended by your soil test.
Mow your grass HIGH. A minimum of 3" promotes deeper, more robust roots and shades weed seeds, preventing them from sprouting.
In cooler weather, using a hand cultivator, remove the dead material in some of the larger spots of the lawn (especially the shady areas) and reseed with the PROPER grass mix. I do NOT mean that you should go down to a box store and buy anything that they sell. You should be able to find a good product online. You should seed shady areas with a mix of fescue and ryegrass. A reputable seed source will list percentages of seed by grass type (and often by variety). Do not buy anything that contains less than 90% of a mix of ryegrass and fescue. Cheap seed = a poor seed mix and LOTs of weed seeds included. When to seed? Often September or October (depending on where you live) are best, because of cooler temperature and more reliable rain. If you live in the deep South, then ignore this recommendation and get local information from your Extension office.
Notes
I see no reason at all to waste your money on sod. Follow the steps I listed and you definitely will not need it.
NEVER APPLY A PESTICIDE indescriminately! Beefore applying a grubicide, you need to make sure that you have a grub problem. Before buying a mole killer, you must make sure that you have moles (I see no evidence of moles in any of your photos).
I do not see a massive broadleaf weed problem. If you do want to treat your weeds, get a backpack sprayer and spot-treat only. I use Weed-B-Gone because it contains three different chemicals, but I use it sparingly. Also, be aware that some weeds (like violets) are not killed by most weedkillers - you want to get rid of them? Then hand weed. It is not a good idea to spread an herbicide on your entire yard. You walk on that yard and, until it rains heavily, you will be dragging pesticide residue into your house on your shoes. If you have a young child playing on the floor...
The final herbicide that you list is glyphosate. Glyphosate is coming under more scrutiny for adverse health effects and may cause cancer if you get enough of it on you or in you. The science on this is currently unclear. What is clear is that glyphosate use leads to weeds that are resistant to it (i.e. no longer killed by it). I personally use glyphosate, but in very small quantities and only when I believe it to be absolutely necessary.
A lawn is an ecosystem and not a green carpet. If you treat it like an ecosystem, you will have a healthy lawn that requires less maintenance.
