Hmm..
I'm still pretty new to building but I've taken great interest in scavenging older parts and reusing them on newer computers where possible. Your budget range seems right in my comfort zone so perhaps I might be able to offer some advice.
1) Mobo + CPU
Your current CPU is still Haswell and uses a LGA 1150 socket, so you'll be fine with any motherboard that will give you the features you require. USB ports is all well and good, but you might also want to consider front USB 3.0, on-board sound, memory slots, SATA ports and the like.
Reusing your old CPU sounds great, and I can recommend the Asrock H81m-HDS (micro ATX). With the newer version featuring USB 3.0 front outlet, it is very relevant and cost efficient. It features 2 RAM slots and 1 PCI-E x16 for the GFX. The M-ATX form factor also allows you room to pick Cases with a smaller form factor to save space.
2) PSU
Personally, Seasonic makes excellent PSUs, and your's is probably fine. However, as you have mentioned that the case was previously rather dusty, I do hope that dust has not accumulated within the PSU. Do see if you could clean it up. It'll probably continue to serve you well for awhile.
Do note, however, that connectors will limit future upgrades. Seasonic's older 620W are only capabel of 6-pin PCI-E power connections. Some higher end GFXs require 8-pins. Hence, when you do upgrade in the future to a better GFX, you can change the PSU then.
3) Casing
Should you decide to go down the M-ATX form factor, there are many more interesting cases you can consider. Bitfenix Prodigy M remains one of the rather sought after cases for looks and function, while Fractal Design Arc Mini R2 gives huge real estate for future GFX and very versatile component layouts.
As you do not look to be doing much heavy over-clocking, air cooling is probably the road you'd like to go. Both cases run relatively silent and have multiple fan options. Fractal has a huge edge in filter placement and cooler compatibility, but Bitfenix takes the edge in design and size.
Either is fine, but as your system does not require intense cooling, any case which catches your eyes online should provide sufficient airflow.
4) Cooling Fans
As I previously mentioned, you do not seem to be doing any heavy over-clocking. As such, your case temperatures should be relatively comfortable to you. Fans could always come at a later date for design flair and slightly better temperatures.
Keep in mind most Mobos have a limited number of fan ports, and be ready to use molex connections from the PSU to power your fans.
That's about it in my opinion. Do feel free to chat me up or leave me any message on my facebook page,
www.facebook.com/kisspc (Keep It Simple). I will be documenting a few builds in the coming weeks, and would like to help many others get their own PCs as well.
I am eager to learn from everyone regarding all matters as well, so feel free to correct me where I am misinformed. Thanks!