I'm looking to get a new desktop PC shortly, for school (word processing and math applications like MATLAB) and for some gaming (Team Fortress and internet games). I've already got a good monitor and all other necessary accesories. For the tower itself, I'll have to start from scratch.

I've got a $500 budget to work with. At best, I would like to be able to run most games on low settings with a high framerate.

Buuut I have no idea what to get, nor have I ever built a PC myself (shouldn't be too hard, right?). Any of you experts mind lending some suggestions?

Go to the nearest shop and tell them your budget, they will give you a list with last gen rip off low specs, post them here and we will edit the list and then you can return to that shop and request our specs.

If you want to build it yourself then it's time to start browsing Newegg for deals on hardware. They sometimes have deals on DIY kits, too. They have guides, as well.

For example

Intel Core i5-6400 6M Skylake Quad-Core 2.7 GHz, Asus Z170M-PLUS MOBO, Avexir Core 8GB DDR4 2133, Fractal Design Core 1000 mATX CASE, Mushkin 120GB SSD, Seagate 1TB Bar. HDD, RAIDMAX XT Series 500W PSU, LITE-ON DVD Burner
A Full Solution Perfect For Any Household ~
In stock. Limit 5 per customer.

was: $550.92

$485.49

http://www.newegg.com/Product/ComboBundleDetails.aspx?ItemList=Combo.2535097

No GPU? I'd go with an i3 instead and maybe a RX470

Just an example.  I didn't even look at it all that closely.  Often the kits are only partial and it's quite possible he won't find exactly what he wants.  

I'd probably go AMD FX-6300 but I don't know what GPU prices are like now.

You could go for a decent cpu this time then get a gpu later. This way you could end up with a better rig overall.

Interesting suggestions so far, everyone. Keep 'em coming!

Here's my quick little suggestion. God the US prices are stupid cheap compared to Canada's

Option 1 CPU: Intel Core i3-6100 3.7GHz Dual-Core Processor  ($124.99 @ Newegg) 

Option 2 CPU: AMD FX-6300 3.5GHz 6-Core Processor  ($105.98 @ Newegg) 

Option 1 Motherboard: Gigabyte GA-B150M-DS3H Micro ATX LGA1151 Motherboard  ($65.38 @ Newegg) 

Option 2 Motherboard: Asus M5A78L-M/USB3 Micro ATX AM3+ Motherboard  ($45.98 @ Newegg) 

Option 1 Memory: Kingston Savage 8GB (2 x 4GB) DDR4-2133 Memory  ($50.99 @ Newegg) 

Option 2 Memory: Kingston HyperX FURY 8GB (2 x 4GB) DDR3-1600 Memory  ($41.99 @ Newegg) 

Storage: Western Digital Caviar Blue 500GB 3.5" 7200RPM Internal Hard Drive 

Case: Corsair 200R ATX Mid Tower Case  ($44.99 @ Newegg) 

Power Supply: EVGA 430W 80+ Certified ATX Power Supply  ($18.98 @ Newegg) 

Optical Drive: LG GH24NSC0B DVD/CD Writer  ($19.49 @ Newegg) 

Total: $355 and after mail-in rebate $324.82

Now it doesn't include a GPU or OS because there are new cheap GPUs coming out soon such as a rx 470 which will be good for 1080p gaming which will cost around $150sh range. Getting one before those come out will be paying more for less

As for the OS, you can get a legit version of Windows for around $20-$40 from kinguin. I never personally used them but a video will show you how it works and etc:

Thanks! I'll look this over carefully. I think I can get the OS for cheap from my school.

Definitely go for an RX470 when it releases.