I usually start by taping up electrical connections and hosing out the engine compartment with either a pressure washer (wide tip moving quickly) or a low pressure hose. I then allow to dry and spray Zep orange degreaser straight or 1:4 onto surfaces (lowes or home depot). Another good degreaser is Meguiars super degreaser available online. repeat except agitate the cleaner to get the finer grease bits off. For agitation, use a wheel brush or a tooth brush for small areas. If you are worried about ruining exterior paint,it is best to either mask off, or rewax afterwards. Don't have pictures of doing my 80' 911, but i do off a saab i did.
Before:
After:
Same products/process also work really well for wheel wells!