Cheapest all grain is probably this method.
https://www.homebrewtalk.com/f39/easy-stovetop-all-grain-brewing-pics-90132/
If you have brewed before you probably have everything already.
If you are going to be doing full boils a burner is your best bet as most stoves will not boil more than a few gallons.
You can get a pair of 5 gallon paint strainer bags from your local hardware store for < $5 usually.
A large pot to hold/boil your wort is necessary obviously.
If you are mashing in your pot, it is not a bad idea to use old comfortors/blankets/winter coats to maintain temps if you are not using something insulated.
That is bare minimum. I have been making beer with a burner, large pot (I find at least 5 gallons more than your batch size is needed if doing full boils), and a second pot to hold runnings or sparge water, a cooler with bazooka screen and valve and a piece of heat resistant hose and an home made immersion chiller as my equipment for over a year now with no trouble and great results.
If you can afford it build or buy for what you want in the long run as you will spend less as a result in the end. Check on craigslist for homebrewers selling off equipment for deals, and if you are slowly building up your equipment you can always sell your old equipment off on CL. Another great resource, at least so I am told (I am not a member of one), is through homebrew clubs.