Code name “Baby”

[rvpopeye]

I feel DeoxIT is better suited to things like circuit board and plug in type connections etc.. It will work but doesn't protect as well from future oxidation like the NoAlox.  I worship the stuff but DeoxIT is fairly expensive for a very small can and NoAlox is way better suited for this kind of stuff IMO because NoAlox has a grease like consistency and will hold up for a very long time in under vehicle environments. Just wire brush to bare metal first .  Some degreaser after opening the ground connections wouldn't hurt either.
I've been there done that (still do) and have seen the results over time . Use a bit on the battery terminals too. 
Now if you want to use both DeoxIT and NoAlox I wouldn't try to stop you , go DeoxIT first after the clean and polish and use No Alox last ..but I really think NoAlox alone would be a best bet.
BONUS POINTS  the container will last you for many future applications.

One more detail on NoAlox . Squeeze the tube a lot to mix it up , it separates over time. You want it to look like an almost liquid gray paste. Not clear, The paste needs the gray part . This stuff was engineered for HIGH voltage/amperage exterior connections. OOOie !  Don't be afraid of getting it on your hands , none of my fingers have fallen off so far in the 40 years I've been using it. (Since the master electrician I apprenticed with turned me on to it.)
DeOxit came out in the mid 80s and was called Cramolin from Caig Labs before NoAlox bought them out so been using both for that long..
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dabdi dabdi dabidit Dat's all folks !