Mini Tower can use standard EPS12v PSU EVGA 700BR or equivalent.

Smaller models cannot use this inside the case because its too big.

https://www.dell.com/support/kbdoc/en-us/000129376

Re: when I install a new psu should the fan be facing inwards (towards the motherboard) or outwards (towards the case)

new psu can only be mounted to case rear side in one orientation because standard  mounting hole spacing is not symmetric. you can not flip the psu upside down to mount it.  aftermarket psu fan is typically intake and rear side of psu has grill for heat exhaust.