For RM3700K without PSU and casing, I'd do the following,

Ryzen 5 3600 RM800
GIGABYTE B450 I AORUS PRO WIFI RM600
Sapphire Pulse RX 5600 XT RM1400
Hyper X fury 16 GB 3200 MHz RM500
ADATA SX8200 500 GB RM400

I assume you are interested in playing future AAA games. If you are just interested in playing e-Sport titles like Dota or CS, then stick with the 3300X. I also assume you are playing at 1080p and 60 Hz, since you did not mention the monitor you were using. Feel free to share your monitor specs so we can adjust the parts to maximize your monitor's usage.

Sapphire Pulse has a good cooler on the 5600 XT, I have the 5700 XT variant.
I recommend the Hyper X RAM and ADATA SSD over the T Force RAM or Samsung SSD because I'd recommend spending money towards parts that improve gaming performance (CPU and GPU) over RAM and SSD. The extra money saved here go towards the CPU. If you do decide to go with the 3300X then the extra money you have go towards the service cost of putting this together. The prices above are from Lazada, so expect higher prices if you have the shop put this together for you. I do recommend you have them put it together, solely for the after sales support in case something breaks down.

It's typical for ITX builds to prioritize casing before anything else, and it's a personal choice so that I'll leave it up to you. The larger cases like the TU150 or the H210 can support a bigger cooler in case you want to upgrade CPU or overclock somewhere down the line. Both support a maximum of 165mm cooler height, so you can use the Scythe Mugen 5 Rev B (RM200). The H1 is much smaller, but the I/O port is at the bottom and it runs hotter than either TU150/H210, but dont worry too much about that since you're just using a 3300X/3600.

If it is for AAA gaming, go with the 3600. You will be good for at least 3 years.
The monitor is alright for 1080p 60Hz gaming so your CPU and GPU selection is good.

I recommend the Fury because that is what I'm using. It has RGB as well and is from Kingston. I have no experience in using T Force so that's your call. Go for 3600 MHz RAM if you can, or 3200 MHZ is good enough if you cant.

As for CPU cooler it's up to you because the R5 3600 is not hard to cool and already comes with a cooler out of the box. So when looking at a cooler, consider if you want to OC or upgrade to a i7/i9/R7/R9 later.
I personally would go for the Scythe Mugen 5 Rev B as it can support high end CPUs up to i9 or R9 if you upgrade later for a fraction of the AIO cost.
If you would like to spend on an AIO, know that the TU-150 supports 120mm AIO while the H210 supports 240mm AIO. 120mm AIO is good up to i5/R5 while 240mm is good for i7/R7. Take a look at your budget and see which one looks nice.
If you want a 240mm AIO, I can recommend the NZXT X52 Kraken (there's a X53 that came out last year, but I dont like the cable management on that).

EDIT:

TU-150 uses an SFX psu.
Your options are Silverstone SX-650G or Corsair SF600/SF700.
Corsair ones are not easy to find nor are they cheap.

H210 uses an ATX PSU.
You have a lot more options here, and ATX PSUs are cheaper than SFX.
I have the RM650 and recommend that or the superflower leadex II/III 650W.