I personally believe having the proper digging equipment is probably more important and will save or cost you the most time, and allow you to enjoy the hunt more and avoid frustration. I think you could get a number of detectors for dry land, a hand probe, and digging tools for under $6oo, maybe under $350. If you have a specific goal, such as under water then the price increases dramatically.
Seventeen years ago, I purchased a Garret GTA 1000. I'm still a fan of it for coins. The value of it in today's market is probably about $100. But it's a 3rd arm to me. My motto is "At least one coin a day, that is all I ask." I'm not sure how many years I've gone on that streak ( Yeah, I'm still finding at least 1 coin a day.) I hunt for coins everyday.
Therefore I will offer my free advise; Investigate how you are going to get coins out of the ground in a timely matter-- quality sand scoop, sturdy digger (I personally use a snap-on pry bar.) There are many quality detectors, too many to name. However, it's not having the right basket or scoop, potentially losing the coin, which will frustrate you.