Right
Your 316i is the same as the 318i bar the crank shaft (just though I'd clear that up

).
The E36 engines up to 1995 are the M42 (which are 1.8 ), post 1995 E36 engines are M44 (which are 1.9).
If you plan on fitting an E36 M42 you need to change the inlet manifold to the E30 one (E30 one is better than the E36 one), you will also need an E30 M42 sump and engine mounts. It's much easier to find and fit an E30 lump tbh.
You need:
1. M42 engine
2. M42 engine loom and ECU
3. M42 exhaust manifold
4. 318iS exhaust system
5. M42 coolant hoses
You should be able to leave the rest of the drive train alone as they use the same gearbox as the M40 (engine code for your 316i and the 318i) so I've been told any way lol! (having problems with mine but seem to be the only one

).
If you pull all ancilleries from your 316i out of the engine bay prior to lift it will make it all easier. You can reach all the gearbox bolts behind the engine and from under the car. You might like to try doing it by undoing the engine from the gearbox, pulling the engine forward and up then dropping the M42 in and back onto the gearbox although lining the two up could be fun! If you have a little more time take the M40 out with the gearbox attached, take the gearbox off and bolt it to the M42 then put the whole lot back in again, depends what you want to do, both have the same amount of faf involved. Doing the latter can be done in a day easily as long as you prep the engine which is coming out like I said (by disconnecting everything and making sure all bolts are loose so you don't waste time trying to undo tight bolts on swap day).
Bare in mind the 318iS (which came with the M42) came with rear disc brakes and you wont have them on the 316i. You might also want to upgrade the suspension.
Hope that helps.