What is the best cheapest unlocked LGA 1150 processor?



The Intel Pentium g3258 is very popular and around 65$.

 
The G3258, is an outstanding cpu if you will overclock it.
The nice thing is, that the lga1150 motherboard will allow you a future upgrade to a i3,i5, and i7.
If you pick a H97 or Z97 motherboard you will be compatible with upcoming 14nm broadwell processors.
 
While it is possible to build something for $450, you have to cut too many corners for future growth. The OP wants to upgrade later, so, to me, that means this system must have the final motherboard, case, and PSU.

Here's as cheap as I would start. No monitor, because you are going to get a second hand pawn-shop one or second hand flat-screen TV and upgrade it later.

PCPartPicker part list / Price breakdown by merchant

CPU: Intel Pentium G3258 3.2GHz Dual-Core Processor ($63.00 @ SuperBiiz)
Motherboard: ASRock Z97M OC Formula Micro ATX LGA1150 Motherboard ($99.98 @ Newegg)
Memory: G.Skill Ripjaws X Series 4GB (1 x 4GB) DDR3-1600 Memory ($22.99 @ Newegg)
Storage: Crucial BX100 250GB 2.5" Solid State Drive ($75.60 @ SuperBiiz)
Case: Xion XON-560 MicroATX Mini Tower Case ($29.99 @ Newegg)
Power Supply: Antec Basiq Plus 550W 80+ Certified Semi-Modular ATX Power Supply ($44.99 @ Newegg)
Operating System: Microsoft Windows 8.1 OEM (64-bit) ($82.98 @ OutletPC)
Total: $419.53
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2015-09-06 11:34 EDT-0400

The CPU can be upgraded to an i7 4790K and the PSU will run it overclocked, and you can add a GTX 970 GPU if you want to. Memory can be expanded too. It will run on 1 x 4.

http://www.tomshardware.com/forum/id-2706290/g3258-memory-overclocking-project-reults.html this is some benchmarks I got from such a system.