Help Are there any stable, fast remote desktop apps for in the same home?

[GoldenSun3DS]

Every remote desktop I've tried is very laggy. Could this be because my desktop is too slow?

It's an HP Pavilion 223W, but I added a GPU and upgraded the PSU (i3-4130, R9 270, 8GB DDR3 RAM, 1TB HDD, 500W PSU).

And my phone is a Galaxy S6, though I haven't tried remote desktop with it.

 

[GoldenSun3DS]

Just did speed tests on my phone:

In megabits:

4G 11.48 down, 9.32 up

WiFi 19.02 down, 1.87 up

I'll speed test my desktop in a minute.

 

[GoldenSun3DS]

Desktop:

WiFi 20.41 down, 1.98 up

Phone hotspot 32.25 down, 16.36 up