A sonarman will increase a DDs ability to see a sub.   If you like ASW (anti-submarine warfare), you should get a sonarman.    

Your next ship, the DDX has been considered the BEST DD in the game for a Number of years.  It is fun, does great in Blitz  with its 5 r-mounts and with HH in the T slot, it can be a great sub killer.

The Gearing remodel is slightly stronger in structure and has a little larger gun space.
However, IMO, its better to go for the DDX and skip the remodel.

I liked the DDX so much that I kept it around until I had no more sailors that could fit
on it.   BO, gunner, and Support sailors got to a lvl where there was no more room.   Even then, I skelontonized crew for a while so I could keep using the DDX.

As to the sonarman, do some searches as the sonarmans range ability goes in steps based on EXP points.   And that is True experience points, not what it shows in the harbor.    There is a formula for determinging this.   It takes into accounts Vets, experts and the posted exp points. 

Another reason for waiting for the DDX is that you will gain EXP points quickly and be into it in short order.

Do what you want.  I had the gearing and used it until I got the DDX.  And I had lots of fun by doing that.

DDs blow stuff up, especially Timerman and DDX. Make sure you use the right guns (7" always) and you can kill any dd/cl and most cas pretty easily.

About the sonarman. If you don't really intend to use one later on a CL for example, you don't really need one just for your DD.  Indeed it will increase detection range but not the low level one you will likely be using.  So an at-level sonar will really be no better than the default detection you get for being a DD.

Remodel - you don't need to because you don't get the remodel credits back.  Usually at lower levels you zip through the ship tree fast enough so you don't end up playing one ship for a prolonged period of time.  For a DD remodeling is probably something you do later when you decide you want to play that ship for fun due to a certain characteristic.

ASW is very beneficial even if you can't attack the sub and just detect them.  Also consider AA.  Good XP and credit gain, beneficial, fairly low risk, and great for learning manual aim.

If you're lucky some guy named Bonaventure might still be out there giving out credits :)

If this is your first time ginding US, for BB I suggest from Gearing:

DDX->Atlanta->Brooklyn->Cleveland(*Skip if you plan on playing blitz)->Baltimore->Alaska(*I highly suggest skipping this or better yet buying a Pensacola)->Remodel Guam (You can try it, but it really takes experience with the game to use it effectively in modern gameplay.)->If your wiling to spend the money (Or win one via an Event) the Sevestopol is a great replacement @ level 61 for the horrid BB1s US has.)->Colorado (The New Mexico sucks in comparison to the Colorado in every way. Completely worth the 5 extra levels to get the Colorado, plus its cheapest USN BB2 as you are not remodeling from a BB1 to a BB2)-> South Dakota (Much easier BB3 to play than the North Carolina for a first time BB grind)->Iowa->Montana->Nebraska

Of course all the EBBs are good replacements to grinding, personal in terms of usablity, USN EBBS rate as follows:

EBB5 Missouri , EBB3 Maryland, EBB4 Washington, EBB5.5 California, EBB2 Missisippi, EBB1 New York, EBB3 Indiana (Seriousness, Indiana is the worst EBB3...)