First off, good for you for deciding on BIAB. Obviously a man of good judgement
A couple points:
Choose a bag that fits your kettle. Either make you own from viole cloth or buy a good one. There is a guy here who goes by Wilserbrewer who makes a very nice product. I use a 29 inch bag from Morebeer.com. I like that one a lot.
Does your kettle have a thick 3 ply bottom? A thick bottomed kettle will prevent scalding or melting of your bag. I do not use any screen or false bottom. Not needed.
A basket is also not needed. Some folks use one, some pull the bag and transfer to a colander over a bucket to drain, some use a pulley system, etc. I just learned a new way that I like. I pull the bag, put an oven rack over the kettle, lay the bag on that and squeeze the bag with the kettle lid. Works great.
I may sound like a broken record to others but I will continue to offer this advice: spend some time reading stickies and posts over at BIABrewer.info
It is a free site with folks that are experts at this process. I learned so much over there and am a more confident brewer because of it. I also use their spreadsheet called the BIABacus. It is also free and is the greatest software for determining how much water, grain, hops, etc you need to make the beer you want.
Lastly, I will just say that many people make 5 gallon batches just fine with a 10 gallon kettle. I owned mine for 1 batch. I realized that if I wanted to mash without any sparging then I needed a 15 gallon kettle. I traded in my 10 for a 15 with a 3 ply bottom and have never regretted it. If you want to sparge (as many do) then a 10 gallon will work great.
Have fun!