Do you have the G1 or the G2 tower?
Verify that the psu fits a standard ATX space.
Measure the rear dimensions.
It should be 150mm x 86mm.
The depth can vary from 140mm up to 180mm.
Because the motherboard does not use a standard 24 pin connection, you will need one of those 24 pin adapters you linked.
Quality counts when buying a psu.
Look for one with a 7 to 10 year warranty.
What gpu is now present?
What gpu would you like to install?
Are you using integrated graphics?
What do you want to accomplish with a gpu upgrade?
A strong graphics card is going to generate heat.
Your case is not a good one for airflow.
The front intake fan assembly Looks to be proprietary, likely, only 92mm.
You may not be able to get more cooling airflow into the case.
Lastly, this pc was designed for windows 7.
If that is what you are using, verify that any modern gpu you install is supported by windows 7 graphics drivers.