You say you are new to sailing but not to waters but apparently you haven't done any off shore boating of any kind. I hope you don't try this without at least having someone aboard that is an experienced hand and at least three people to help with watches because nothing substitutes for experience and the only way to get it is to get it.
Radar Only if you think there may be fog and then if you do, stay in port until it clears.
Depth sounder Absolutely, but only when you are entering and leaving port in most cases.
Chart plotter Indespensible, in my opinion, at today's prices.
Life saving equipment Absolutely and don't stop with just the minimum required by the CG.
VHF radio Absolutely Both an installed one and hand held one.
Binoculars Yes, a good quality pair
A GPS and set of paper charts of the area you will be sailing is also critical.
Finally, make sure that everyone that stands watch knows exactly how to tell if you are on a collision course with another boat and can stay alert at all times!!!!!