The stripped lower receiver is the only part which requires an FFL transfer. Lower parts kit, uppers, bolts, etc can be purchased through the mail or any stocking shop.
One cost savings is the taxes you pay. A firearms tax is levied on the firearm purchase. If you buy a stripped lower you pay the tax on just the lower (tax is included in the price). A lower goes for anywhere around $110 - $175. If you purchase the entire firearm then you are paying firearms tax on about a $1,000 item.
If you are only building one rifle you will likely spend more on tools then what you will save. A hybrid approach is to buy a complete lower receiver assembly, and in a separate transaction on a different day buy a complete barreled upper assembly. Some uppers include the bolt carrier and bolt, others do not and you have to buy in addition. If you get a flattop then you need a iron rear sight (BUIS) and/or an optic sight.
If you are planning to build a few rifles then getting the basic tools (can't remember, maybe $50 - $100) is a good investment. AR15.com has excellent tutorials on every aspect of assembly options, tools and detailed photo instructions.
My first AR15 I bought a DPMS complete lower assembly, and later a complete LMT upper and a bolt carrier group, and Troy rear folding BUIS. This was before the election when complete uppers and lwoers were plentiful.
For the next few rifles I bought Rock River Arms and a Double Star stripped lowers (what was available), RRA lower parts kit and butt stock assemblies (includes buffer assembly). I got another couple of LMT upper and BCG, with LMT or Troy BUIS, and the last one is waiting for an upper. I was piecing them together as I had funds and as parts became available for a reasonable price (very spotting earlier this year).
I would build a rifle if I wanted a configuration not available as whole rifle, or if funds and parts were limited and I wanted to spread it out over a period of time. careful though. I bought a stripped upper receiver thinking I could build it up. But it has been hard to find the barrel assembly I want as most barrels are being sold in complete upper assemblies (more profit and wider market). It is easier right now to buy a complete barreled upper receiver than to but a barrle on its own.
Stripped lowers, parts kits, and butt stock assmeblies are fairly easy to find once again.
ETA: An AR15 lower receiver can be used with uppers for 5.56/.223, .22LR conversions, 6.8 SPC, 7.62x39 and similar short cartridges. You need an AR10 sized lower for the longer .308 sized cartridges (.243, .260, etc.).
