If this car is new to you, and you don't know much about its recent service history, then you'll want to start with the diesel basics.
If the fuel lines look old, then plan on replacing all the rubber lines you can. I would use quality German hose or specialty sourced viton lines.
Fuel filters. There should be two filters in the engine compartment, and a tank strainer. The latter is a pain to remove, but most of these are fairly clogged by now with rust and algae.
Air in the fuel system can lead to problems starting and poor performance. The fuel lines can contribute, but one of the biggees at this point in time can be the original fuel primer plunger on the top of the fuel pump. The originals have a knurled plastic knob on top. If you unscrew this and lift the plunger up, often fuel will leak out; that's a point for air to enter the fuel system.
The replacement Bosch plunger is just a black plastic push cap. Highly recommended.
Diesel is a compression ignition unit, so compression is a big deal for starting and running. Two things you should check with regard to the basic engine are adjusting the valves and determining the stretch of the timing chain. I recently adjusted the valves on an OM621 and OM617, and of the eighteen total valves I checked, only two were set to the proper clearance--the rest were too tight. Tight valves can lead to reduced compression and starting problems. While you have the valve cover off, you can set the engine to TDC for #1
cyl and check to see where the camshaft gear is in relation to the crank gear; this tells you how much the timing chain has stretched. I don't remember the specs for an OM615, but anything over something like six degrees of stretch is going to require a new chain be rolled in.
If your engine still uses the loop style of glow plugs, you'll want to remove all the connectors and buss bars, and check each to determine the resistance values. Any plugs without continuity to the block will be dead. Personally, I'd preemptively plan on replacing the loop style with newer pencil tips, which glow hotter and are easier to diagnose when in service.
The previous advice about battery and starter condition is also important for starting performance.
There are also some other tips about throttle settings, injection timing, etc. but these are the basics I use when approaching one of these old machines.