ReyMart Eyeless

If your on a budget look at B450/Ryzen CPU's. They are a good value. Though depending on your workload you may want Intel. On a side note, we are eventually going to be graced with DDR5 at some point in the future. I believe it might have been released on the server side, though dont quote me on that. 

Whats wrong with your current board? Because if your going to upgrade a new motherboard I would just upgrade to a new platform. Also DDR3 works just fine in most case currently. Not sure what your so excited to go to DDR4. 
 
Its Haswell NOT Haswell E. Haswell E is the server side of Haswell, and Intel at least back then the server side was a generation behind the desktop market. Remember servers need to be reliable and putting current gen hardware is not a good idea. But using hardware that is a year old and is proven is much better. 

Oh okay

DDR3-1333/1600, DDR3L-1333/1600 @ 1.5V
 
Thats what officially supported on that CPU via intel: https://ark.intel.com/content/www/us/en/ark/products/75047/intel-core-i5-4670-processor-6m-cache-up-to-3-80-ghz.html
 
Back in the OLD days when Intel's memory controllers were on the north bridge there were motherboards that supported two different memory standards. I think this was in the DDR and DDR2 days. But it came with several restrictions. However now days the memory controllers are built on the CPU and thus Intel will only support One generation of Memory at a time generally. 

what all parts do you have now?
 
If your system is working, id just save up for a ram +  cpu + motherboard upgrade all at once.

Correct.

Besides the motherboard issues because DDR3 and 4 slots have different numbers of pins and the notch is in different areas. On pretty much all newer CPU's and i5 4670  would be this way as well, the Memory controller is built on to the CPU. Im pretty sure the memory controller would have to support DDR4 as well. The first Intel Chips to support DDR4 was Haswell-E, I think that's server grade if I recall correctly.    

Which motherboard has DDR4 support and an LGA1150 socket?

yes, and the cpu wont be compatible. 
the oldest consumer ddr4 board from intel is z170/b150/h110 with sky lake. and you're running haswell. meaning you can't.

There is no possible way to use your CPU and motherboard with DDR4.  If you want to use DDR4, you absolutely have to change out both your motherboard and CPU.

what do you exactly mean by that? 
you can't use ddr4 dimms with a ddr3 cpu.  
the imc can't work with it.

I can't, because there are no motherboards that support DDR4 that also work with that CPU...

the imc can't and the dimms on the board can't since it's a different pin layout.

There are no motherboards for the i5 4670 that support DDR4.

you cant. Different pin outs and slots from DDR3 to DDR4 and the controller on that chip doesnt support DDR4 anyways. 

PCPartPicker Part List Type Item Price CPU AMD Ryzen 3 3200G 3.6 GHz Quad-Core Processor $99.00 @ Amazon Motherboard Gigabyte B450M DS3H Micro ATX AM4 Motherboard $72.99 @ Best Buy Memory Patriot Viper 4 8 GB (2 x 4 GB) DDR4-3000 CL16 Memory $41.99 @ Amazon Storage TCSunBow X3 240 GB 2.5" Solid State Drive $27.99 @ Amazon Case DIYPC Solo-T2-BK Black USB 3.0 ATX Mid Tower Case $33.98 @ Newegg Power Supply SeaSonic S12III 500 W 80+ Bronze Certified ATX Power Supply $54.99 @ Best Buy   Prices include shipping, taxes, rebates, and discounts     Total $330.94   Generated by PCPartPicker 2020-07-29 15:41 EDT-0400   this is the best for your budget but would not recommend. Will struggle with streaming and gaming. you should either get a console or buy used

This is the best you could do. For a a decent streaming and gaming machine, you would need something like this.
PCPartPicker Part List Type Item Price CPU AMD Ryzen 3 3100 3.6 GHz Quad-Core Processor $109.99 @ B&H Motherboard ASRock B450M PRO4 Micro ATX AM4 Motherboard $82.99 @ Newegg Memory Team T-FORCE VULCAN Z 16 GB (2 x 8 GB) DDR4-3200 CL16 Memory $57.99 @ Amazon Storage Crucial P1 500 GB M.2-2280 NVME Solid State Drive $59.99 @ B&H Video Card Gigabyte GeForce GTX 1650 SUPER 4 GB OC Video Card $159.99 @ Newegg Case Phanteks Eclipse P300A Mesh ATX Mid Tower Case $59.99 @ Amazon Power Supply SeaSonic S12III 500 W 80+ Bronze Certified ATX Power Supply $54.99 @ Best Buy   Prices include shipping, taxes, rebates, and discounts     Total $585.93   Generated by PCPartPicker 2020-07-29 15:32 EDT-0400   (about 29,000 pesos). Yes PC hardware is expensive

use pcpartpicker and look what you find i would go with a ryzen 3 2200G or something like that
 

That's a new one for me didn't know that the report function had "posted in the wrong subforum"

yha
 

what is the buget?

We have report function for a reason. And I've been moving threads from GD better part of today.

whats your budget?

we really need a set budget if you want a real recommendation.