Hello.  I would like to replace the PSU in my 2010 HPE-210 desktop computer. HP describes the case/tower as "mid-size ATX" and the existing PSU is a Bestec ATX0300D5WC B and it is top-mounted. 
I've not done this before so please excuse my ignorance.
 
Will EVGA PSUs fit this case? I'm considering the 450W b3. The Bestec dimensions according to sites that sell it are: 

• ATX Form factor
• 6" Wide X 3.5" Tall X 5.5" Deep     (I attached pictures but don't see them in the preview) Thank you. 

It should work fine. I recommend if you have not done a PSU change out take pictures or video of everything you removed power from to help you remember. The most important fan is going to be to the CPU which should be a big tower on the motherboard. Make sure that has power before you turn on the system though it is probably plugged directly into the motherboard which is fine but I have seen some prebuilt systems using a fan connected to the PSU.  Really any fans is going to be important part. If something else isn't powered then it just will not work but to not have the cooling working means bad things happen very quickly.
 

One thing to consider is that a lot of pre-built systems use proprietary power connectors to power the motherboard, these days.  You should check what connectors are plugged into your motherboard (normally a 20/24pin ATX connector and a 4 or 8pin ATX/EPS power connector.  However, some Dell/HP/Lenovo motherboards may use an 8pin (or close to 8pins) connector to power the motherboard (and no 20/24pin), which is different than the 8pin connector used for graphics cards or CPU connectors.
 
These proprietary connectors will make connecting a new power supply a hassle, so you should first check to see if you'll run into this problem.  There are some adapters that can be used to make a regular power supply work with these systems, but it's not ideal.