What size and what type of power supply would I need?

Mini Tower or Desktop? It makes a BIG difference.

http://www.dell.com/us/en/business/desktops/optipl...

Edit-

Now I understand what you meant when you said the 400W power supply "wouldn't match up". That systems motherboard uses a 24 pin Micro-Power connector. That system can use a standard ATX power supply, but you'll need an adapter for the 24 pin connector. It looks like this-

https://www.directron.com/hp24mini.html?gsear=1

Make sure you install the GT 730 into the Blue PCI-E x16 slot...the Black PCI-E x16 slot is wired x4.

http://sites.fas.harvard.edu/~phys191r/Bench_Notes...

The GT 730 only consumes 30w to 40w of power and that's when you're playing games or watching videos. You should be able to boot up the system with the stock power supply. If all parts were up and running at full load then it would come close to the maximum capacity of the stock power supply and that's when you're running a risk of the system shutting down .

Pretty much any Power supply you can buy online follows the ATX form standard so they are all the same. The problems with finding a new power supply arise.It seems like you have the flat desktop version so you would need to figure out the form factor of that power supply then find one that matches.

If the motherboard is a standard sized mATX board, you can always find a cheap ATX case then transfer all the parts to that case. Then you would be able to use a standard sized power supply. Dell has a nasty habit of using proprietary parts so you'd have to verify they you have a mATX motherboard.

Dell is famous for using non-stock parts such as power supplies. You may have to buy a power supply from them or do some handy work of your own to attempt to fit an ATX power supply into the Optiplex case.

psu sizer app online. i use the one on the lower left of newegg's power supplies page