Funnier26

Heyyo,
 

w00t! A fellow gamer of World of Warships. She's a lovely game, but much like the other WarGaming games on the BigWorld Engine? She's not multi-threaded very well so a Quad Core CPU (Intel i3 or i5) is the sweet spot for price to performance and Intel over AMD for that instructions per clock which will matter more since this game is single-threaded.  

It is a good list, but the OP said he wants to order all the parts via Newegg so had to change the filters amigo.
I changed the ram to a parametric filter which selected the Muskin 8GB (2x4GB) DDR3-1600 module which works out better since it's only 1.35Volts versus the G.Skil 1.5volts so it'll run a little cooler for the same CAS latency of 9.
For motherboard? Ehh, no need for a Z series motherboard since it's a non-overclockable CPU. I went with a B85 series motherboard for around the same price since they offer a little more than the H81 series suchy as 4 RAM slots vs 2 as seen here:
http://www.ukgamingcomputers.co.uk/difference-between-h81-and-b85-chipsets-a-33.html
I changed the case to the one the OP picked as it is his choice and it's an alright one.
I left the power supply as that EVGA 500W 80+ Bronze since it's easily the best deal for that price.
I changed the GPU to a Gigabyte branded R9 280. I've had some bad luck with Sapphire in the past is all so it's just brand preference. Gigabyte also has a really good RMA process if you ever need to get the part repaired under warranty.
PCPartPicker part list / Price breakdown by merchant
CPU: Intel Core i3-4160 3.6GHz Dual-Core Processor ($119.48 @ Newegg)
Motherboard: MSI H81M-P33 Micro ATX LGA1150 Motherboard ($43.98 @ Newegg)
Memory: *Mushkin Stealth 8GB (2 x 4GB) DDR3-1600 Memory ($47.99 @ Newegg)
Video Card: Gigabyte Radeon R9 280 3GB WINDFORCE Video Card ($162.98 @ Newegg)
Case: Xion XON-560 MicroATX Mini Tower Case ($29.99 @ Newegg)
Power Supply: EVGA 500W 80+ Bronze Certified ATX Power Supply ($53.98 @ Newegg)
Total: $458.40
Prices include shipping, taxes, and discounts when available
*Lowest price parts chosen from parametric criteria
Generated by PCPartPicker 2015-05-25 14:33 EDT-0400

The r9 280 is way more powerful than the 750Ti and the i3 is better than the Pentium (some game require 4 threads to run, and since the i3 has HT it will work on it). That's the main reason of getting an i3 over a pentium : hyper threading. Sometimes it's required.
 
You seriously don't need a Z87 mobo for a Pentium...nowadays mobos don't matter that much. You most of the time just want the mobo with the features that you require. On budget, it doesn't really matter. Just a decently cheap one.
H87 is just Z87 without OC abilities.
H81 doesn't support SLI , only has 2 RAM slots, no RAID, less SATA 6Gbps , etc. These kind of things shouldn't matter in a budget build, unless you plan on upgrading later.
 
Anyway, here you go:
PCPartPicker part list / Price breakdown by merchant   CPU: Intel Core i3-4160 3.6GHz Dual-Core Processor  ($99.95 @ SuperBiiz)  Motherboard: ASRock Z97 Anniversary ATX LGA1150 Motherboard  ($72.98 @ Newegg)  Memory: G.Skill Ares Series 8GB (2 x 4GB) DDR3-1600 Memory  ($49.99 @ Newegg)  Storage: Seagate Barracuda 1TB 3.5" 7200RPM Internal Hard Drive  ($44.10 @ SuperBiiz)  Video Card: Sapphire Radeon R9 280 3GB Dual-X Video Card  ($162.98 @ Newegg)  Case: NZXT Source 210 (White) ATX Mid Tower Case  ($35.10 @ SuperBiiz)  Power Supply: EVGA 500W 80+ Bronze Certified ATX Power Supply  ($37.99 @ NCIX US)  Total: $503.09 Prices include shipping, taxes, and discounts when available Generated by PCPartPicker 2015-05-25 13:53 EDT-0400   Get whatever case you want, and maybe throw in an SSD.

This is better :
PCPartPicker part list / Price breakdown by merchant   CPU: Intel Core i3-4160 3.6GHz Dual-Core Processor  ($99.95 @ SuperBiiz)  Motherboard: MSI H81M-P33 Micro ATX LGA1150 Motherboard  ($42.99 @ Directron)  Memory: G.Skill Ares Series 8GB (2 x 4GB) DDR3-1600 Memory  ($49.99 @ Newegg)  Storage: Seagate Barracuda 1TB 3.5" 7200RPM Internal Hard Drive  ($44.10 @ SuperBiiz)  Video Card: Sapphire Radeon R9 280 3GB Dual-X Video Card  ($162.98 @ Newegg)  Case: NZXT Source 210 (White) ATX Mid Tower Case  ($35.10 @ SuperBiiz)  Power Supply: EVGA 500W 80+ Bronze Certified ATX Power Supply  ($38.70 @ SuperBiiz)  Total: $473.81 Prices include shipping, taxes, and discounts when available Generated by PCPartPicker 2015-05-25 13:01 EDT-0400

This feels weird, I was in almost the exact situation a year ago. I also had the same avatar and the same monitor...

Get a i3.Pentium is dual threaded and i3 are quad threaded.Please get a i3.Also cheap out on motherboard

@LinusTech Best video since scrapyard wars.