I sent you a friend invite on Steam to help you out, but you didn't accept. Guess I'll continue posting here!

Man, a 1070 is a lot of money down the drain for only playing TF2.

I forgot to ask what case you have. I'll go with mATX for now!

PCPartPicker part list: http://pcpartpicker.com/list/rRzg99
Price breakdown by merchant: http://pcpartpicker.com/list/rRzg99/by_merchant/

CPU: Intel Core i5-6600 3.3GHz Quad-Core Processor ($213.99 @ SuperBiiz)
Motherboard: Gigabyte GA-H170M-D3H Micro ATX LGA1151 Motherboard ($89.88 @ OutletPC)
Memory: G.Skill NT Series 8GB (2 x 4GB) DDR4-2400 Memory ($39.98 @ Newegg)
Total: $343.85
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2016-09-25 23:50 EDT-0400

i5 6600 since clock speed in TF2 matters and you don't have a tight budget. New RAM because DDR4 on Skylake, and unless if you have a valid reason for more than 8GB of RAM then it's best to save the $30-40.

If you buy any recent processor, then yes you will need a new motherboard. A new CPU will help you immensely in other games as well.

I'll ask the Setsul questions: Overclocking yes/no?
Budget?
Any games besides TF2?

I recommend we move to the PC Build Thread so not to hijack this thread.

Hey there, hopefully I can help you out a bit!

First, I'd recommend you download this and check your temperature of the CPU/GPU in idle and on load please! http://openhardwaremonitor.org/

Yes you can upgrade and get a boost in performance, but you're not gonna be able to "stay above 120fps without using a config." Valve makes it hard to do that in a (9?) year old game!
If you are streaming 720p@30fps I think you could make do with an i5 still. On your socket you could upgrade to an i5 2500 or i5 3550/3570 used and get a reasonable boost but it's probably not worth it. If you are really adamant on playing TF2 without a config, you will either have to lower your expectations or build a whole new PC.

If you do decide to build a whole new PC check out the PC Build Thread

#2 Just a heads up the i5 4690k is on a different socket and even if it was, it's on a locked motherboard so no point in a K CPU!

Assuming you are talking about TF2, and that "spiking" means FPS drops, then it is your CPU. It is a big bottleneck. Even for a 760. If Source games are your main priority, then you can consider an i3 4170 and a micro ATX motherboard as a "cheap" upgrade. Feel free to drop by the PC Build Thread

If Source games are chugging, it's your CPU.