i want to replace the cheapie fork i have right now, but in shopping for a new one what numbers/dimensions do i need to know?

make sure the diameter of the tube of the fork matches. (i.e. 1 1/8 to 1 1/8 or 1" to 1") I bet you already know this.

Second, you want to google what the rake of the fork is (rake is the offset of the fork). This is hard unless you have A. Proper tools (don't know exactly which ones)
or B. Know the manufacture's specs.

If it is a recent bike, the make of the bicycle will most likely have a spec sheet.

Try googling it though or post on Bikeforum exactly what year/model/make of the bike and maybe someone else already has done a fork transplant.

Steerer diameter
Steerer style (threaded/unthreaded)
Steerer length*
Fork rake
Stiffness (ridgid for offroad or racing, flexy for long distance comfort)
Wheel/rim size
Tyre clearance/Caliper brake drop.
Fender fittings/clearance

axle to crown length too. especially for MTB suspension corrected forks and stuff.

What kind of bike is this?

it's an older fuji - road

Fork length is important for road bikes as well. Carbon forks are almost always longer than full metal forks - a longer fork will raise the front end of the bike and slacken head/seat angles.

https://www.sheldonbrown.com/rinard/forklengths.htm