New hemi install total cost

Since the above post is almost exactly what I did, I can take a stab at it, though I know I'll forget things.

I got a broken core engine that dropped an intake valve and needed a sleeve. However, I'll just throw out a typical number for a decent working engine of $1500. I think I was probably in ~$1000 between buy the engine, machine work, and a new head.
Swap motor mounts (from TTI), were around $250 I think.
You can use factory log style manifolds with a little work (I didn't, so I added $700 for headers).
I had a 4 speed already, so I bought a conversion flywheel and new clutch (could have reused old clutch, but didn't think it was up for the job) $300 for the flywheel at the time, $200 for the clutch kit

At the most basic, you need motor mounts and a transmission conversion to physically install the engine in your car. Assuming you purchased a fully working engine with electronics, you only need to sort out a fuel system. You could get by with an external high pressure pump and Corvette style filter/regulator combo. I think the filter/regulator was around $60 and the pump probably $200 if I had to take a wild guess (put a carb on mine first, then swapped to Megasquirt fuel injection later).

I know my final tally to have a running carb'd, MSD ignition 5.7 running in my car was under $5000, but I also had to swap power to manual steering, I went to manual brakes (not technically necessary, but more space to work with) and had other parts that weren't strictly necessary.

My best guess at cheapest possible would be $2500 or less. $1500 for engine, $130 for flexplate, $300 for fuel system, $75 for 45 degree oil filter adapter (if you can fit it, I went fully remote with a Summit Kit and block-off plate instead), and the rest for incidentals like radiator hoses, wires, etc. If you have harness and ecu you don't have to pay anyone to strip it down and only use the wires you need, but most people will send it away to get cleaned up at a fairly substantial cost.

The long and short of it is that there really isn't a single low number as it depends what you have in your car already and what you want to keep. If you already have manual steering and a good radiator I bet you could do it for $2500 or less, but most people will want to swap for a better radiator, get headers, go in-tank fuel pump, etc. It can easily add up. I tried to go as cheap as I could because I just wanted a new engine in an old car. I didn't care if it was super pretty or anything, I just wanted to drive it. I didn't get any electronics with mine though, so I had to buy an intake and MSD setup to run the spark, so I was in for $1200 right there.