I'd like to have a healthy consistent lawn. If you really want to fix your lawn up, you want consistent grass types, and few to little weeds. There's a lot of info I could give you but it depends on what you want for a lawn. What are your lawn goals? But it also comes down to how much time and money do you want to devote to your lawn.
Things you need to do first:
- Try to identify your grass types. Take some samples and do some research here and here.
- Try to identify your weed types. I don't know of an all-in-one weed identifier but you can check your local extension office for a list of probable weeds or just start google image searching and checking "lists of weeds" based on your area.
- Invest in a hand-can; a gallon pump sprayer that you will use to apply weed killer(s) selectively. They run about $10-$50 depending on what you get. Home Depot or Lowes or Amazon.
- If you don't have a bag for your mower, get one because you will need it occasionally if your grass gets too tall before you can cut it. You don't want tons of clippings laying around. A normal amount mulched up is fine.
Once you ID your weeds and grasses, you can start applying grass-safe weed (only) killer selectively (only where needed, not all over the lawn). 24-D is the most common broad spectrum weed killer ingredient found in most plain weed killers. Some tough weeds may need a different herbicide but you won't know till you ID them.
Bagging is best when you are cutting thick, overgrown grass since it will not mulch properly and lay on top of the lawn rather than getting mixed in.
This can introduce the perfect habitat for fungus or other disease issues. Yes, you will reduce weed seeds when bagging but that's not the real point.
Effective weed control is what reduces weeds and weed seeds in the first place.
Again, you should bag if you are cutting a lot of thick grass at once but also try not to go more than 1/3 of the blade. So if you were on vacation and missed a mowing, make two passes, lowering the height between and bag at least the first go round. The other time to bag is before you aerate / overseed. You don't need to add to the thatch layer (in fact you might want / need to de-thatch prior to aeration and overseeding).
What you should do:
- Get a soil sample tested so you know your soil makeup. Or at least do some digging and determine if you have clay, loamy or sandy soil. My guess is clay unless you're near the coast.
- Aerate your lawn if it appears compacted (rock hard).
- Overseed your lawn based on what type of grass you already have. That is, if you are happy with that type. If you are looking to start fresh there's a different method / mentality involved.
- Apply some milorganite (organic nitrogen fertilizer). Read the bag for application rates. Normally 15lbs per 1000 square feet. So about one 36lb bag for a little over 2000 sq feet. You can go a little heavy since it's an organic, it won't burn your lawn.
- Irrigate by hand or with sprinklers and aim for 1" of water/rain per week. Deep infrequent > quick frequent waterings. A rain gauge helps with this.
That's enough to get you started. The basic idea is kill the weeds you don't want. Nurture the grass you do want so it takes over. Keep it healthy with fertilizer and mow regularly not taking more than 1/3 of the blade off at one time.