As some people have said - BIAB is just another method of AG. What I think you are primarily talking about here is stovetop BIAB as mainly described by NickJD. A worthy way to start out an AG career without spending any/much cash.
But you say you have some cash to spend - so you have some choices. You could go full sized BIAB - which is the simplest and easiest way that I know of to brew AG. But it does mean buying a bigger pot (or acquiring a keg and modifying it) and most probably a burner. This is the course of action I strongly recommend if the plan is to get into AG brewing regularly. Why?? Because BIAB is the most newbie friendly way to brew that I am aware of - to be sure, other ways of brewing aren't really that hard - but BIAB is the easiest. Full size BIAB being even easier than the stovetop methods... you basically buy your simplicity with the bit of extra cash. You are talking 1 pot, 1 bag, 1 water addition, no sparging, no dilution simplicity - but a bit of cash for the pot.
The best part is, if you do decide that you want go with a multi vessel system later - you haven't actually spent any money that you wouldn't have spent anyway. What did you buy? A pot that you need to buy anyway. So its a no loss proposition.
If you already have a 19L pot.. then I reckon you should
1. - buy some voile, make up a bag and have a crack at either some smaller batches of "plain" BIAB - or use NickJD's stovetop method if you want to brew bigger batches. Cost... less than $10
2. - Buy a 60L aluminium pot, a 3 ring burner and some voile for a bigger bag. This will give you a BIAB system capable of making full AG. Perfect for single batches and capable of pushing out a double batch with a bit of care. You may decide to never move on from this - you certainly don't need to. With that system you can make every type of beer and plenty of it at top quality. Cost - $150-200
3. - If you do decide to move onto a multi vessel system. Then you already have your burner and boil kettle - you just need to decide on your mash tun and HLT. Cost - sensibly another $100-$200 depending on your choices. There is no real upper limit though. You can spend thousands if you decide you want to. Hell my mash tun alone cost more than $700. I love it and all - but the beer is not really any better than when I was using an $11 plastic tub.
Its a nice progression through cost and it allows you to stop, spend as long as you want on each step (or stay there permanently) and move on if and when you are ready and have the cash. My personal opinion is that step one is exactly that - a stepping stone. Except in quite special circumstances, you are very unlikely to stay with it in the long term, you will most likely move on to step 2 or 3 - and I think you are more likely to brew better beer when you do. Steps 2 & 3 are legitimate final destinations in their own right... but unless you are an unusual fish indeed, no matter which choice you make, you will be tweaking and modfying your system for years to come - its all part of the fun.
First things first though -- Do you have fermentation temperature control?? ie: a fridge with a tempmate or something similar. If you don't, then that is where you should be spending your money - not on AG. You will get a better return in quality improvement of your beer by getting temp control and sticking with extract/partials than you will by going AG and having no temp control. Sorry to be a wet blanket at the AG recruitment party... but its the truth.
Cheers
TB