I have a 2004 GS500F that has been neglected by previous owners. The engine exterior has thick layers of what looks to be grease, grime, dirt. What would be the safest way to clean this?

I was thinking just liberally spraying engine degrease over it and wiping it/spraying it down with water.

Will that harm any tubing or plastics, or are there better cleaning methods?

Just go to a manual car wash.
The pressure they operate at won't hurt your seals, still removes grease (with the "soapy" water).
Stay clear of the 'O' ring chain, though!

I don't like those pressure  washers.  If you want to do it yourself just spray it with degreaser wait half an hour and rub it down with an old kitchen brush and then wash it down. As atesz  said - oil your chain afterwards.

Hi all ,  +1  to  Bmf 

Yeah, I have some engine degrease and a stainless steel bristle brush I can use to get between the heatsink fins. Thanks for the info.

Hi Iarn ,  I would use  nylon bristle brush  or  plastic bristle brush  ( not  stainless  steel bristle brush )   any brush that does not scratch aluminum  i.e.  harbor freight salvage  sells  nylon bristle brush , I use everyday on aluminum gearbox cases in boats

Stiff paint brush & mineral turps.

Hi Fector56   , yes indeed   +1