In my opinion BIAB is king for homebrewing with Batch Sparging right up there with it. IMO it is the perfect combination of an easy quick brew day while still having the flavor and customization of all grain. My process evolution
: Mr Beer Kits, Extract + Steeped, 3 Gallon BIAB, 5 Gallon half assed fly sparge, 5 gallon Batch Sparge, now settled in at 5 Gallon BIAB. Pros
1) Minimal Investment: You can buy a bag for less than $30 (check out the Brulosophers review of the brew bag, just bought one myself, bit of a discount with his code). Presumably you already have a kettle and no mash tun is needed.
2) You can produce all grain beer as tasty as a traditionally sparged batch.
3) You don't have to worry about your sparge pH
4) Less to clean. No mash tun and all.
5) You save time by not sparging. Cons
1) Relative to sparging: BIAB/No Sparge methods result in a bit lower efficieny (at least in my experience). But still, I'd rather use another $1 or $2 of grain to compensate and have a smoother brew day.
2) Relative to extract: You need to pay attention to things you don't need to with extract like your water and efficiency. The good news though is Brun Water is cheap, the forum is fantastic for helping you straighten out your water, and you can find decently priced pH meters. Flavor minerals are less important but at a minimum it helps to measure your mash pH and adjust it up or down with acid or baking soda. As far as efficiency goes if your batch comes out a bit stronger than predicted you can always add a bit more water to the boil or some DME if it comes under. After a few batches you should be able to make decent predictions.
There's a nice old video by Brewing TV/Northern Brewer that gives a solid overview of method:https://www.youtube.com/watch?v=o6WVul6IEKk
The Brew Bag website also covers some stuff like grain absorption. You will loose a few degrees during the mash if you BIAB in the kettle - 2 approaches that work for me are leaving the burner on real low and stirring periodically or mashing in a circular cooler with a bag. Some bags filter better than others - I've left the trub and had no issues but also have filtered the wort after the mash, and just recently bought a finer bag.