as someone stated, a degreaser with hot water from a normal hose sprayer is sufficient - I also have access to these items at work
a light brushing on stubborn/heavy deposits is fine, just be aware of electrical connections, distributor, etc...blow off with compressed air and hit any missed spots again
judging from your first photo you're gonna want to clean up your battery terminals - get em nice clean and shiny, retighten and spray with corrosion block or a little light grease to prevent future corrosion