From a quick look at your photos, there is very little actual turf grass remaining in a very lush field of weeds :-) It might be easiest for you to kill off everything and just start over. A couple of applications of glyphosate a couple of weeks apart and you could be good to go!

But when is the best time to do this is going to be location dependent. Spring is not an ideal time in many areas to renovate and reseed a lawn, although sodding or hydroseeding could be viable options. A geographic location will get you better suggestions. Based on the background plantings/trees and the weeds it looks a lot like a Pacific Northwest location......yes?

@gardengal48 (PNW Z8/9) Yes, you are correct. It is in Western Washington near Seattle.

Thought so :-) And that does make a difference, as spring lawn renovations in the PNW is one of the few locations where this is applicable. The suggested window for this is between mid April and mid May. So you might want to start with the weed eradication soon. Not sure what YouTubes you may be looking at (some are decent - many are cr*p) but once the weeds have been dealt with, if you feel comfortable enough with their direction, you should be able to manage this yourself.

Because the PNW climate and growing conditions are pretty unique, regional sites or resources are going to be most appropriate. King County actually has an excellent lawn care publication that provides all the pertinent info. And Swanson's Nursery has a very helpful lawn care calendar.

Personally I would put the projects on a piece of paper and then rate them according to what is necessary to make living in the house better, including yard projects. If when you have the list, and the yard is more important than projects in the house start with the yard.

When we have moved in to "new" houses there were many projects in the house that needed our time and money. If that is the case I would spread some contractors grass or similar mixture, and mow the results, until the yard comes to the top of list.

The last time we move one yard project got high priority and that was a storage shed. The last few years and yard projects have come to the top. so during the proper time periods I have been working on the yard.