Since you have posted this on the PVE sub-forum, I will limit my comments to co-op/operations gameplay. Also, given your preferences and low battle count, I will further limit this to USN, and KM cruisers and battleships tiers 4-7.
USN battleships are Texas, Arizona, and West Virginia. The biggest issue with USN battleships in PVE is speed. Texas might be a good choice when it is top tier, but when bottom tier you will be watching your fellow captains sink the red bots, and hope that they mess up (severely) and leave you something to shoot. Arizona and West Virginia have similar issues, but their saving grace is that they can be used in operations, but even in operations I would prefer the Colorado. In short, I would not recommend any of the USN BBs for you.
On the USN cruiser side there are: Marblehead (Lima,) Atlanta, Boise, and Indianapolis. Of these the Marblehead is a variant of the Omaha, so if you really liked the Omaha this is a great choice. The downside is that you will be up-tiered frequently. This does have the advantage of additional rewards and really teaches you how to play cruisers, because if you make a mistake you are going to pay. The Atlanta and Boise are solid choices. Indianapolis is a good USN heavy cruiser, but Boise is a better choice for a newer player because of her heal. Atlanta is a solid choice if you like spewing HE. It will teach you how to play light cruisers (angle, use cover.) Boise, is more middle-of-the-road cruiser. Boise will teach proper ammunition selection and how to run a cruiser, and because of the repair party, you often get a second chance if you make a mistake. You could also use Boise in a pinch to re-train battleship captains, since many of your battleship captain skills will work on her.
On the KM (German) cruiser side there is the Graf Spee. The Graf Spee has big guns. She is a battlecruiser and plays more like a battleship than a cruiser. At tier 6 you can also use her in operations
KM battleships are: Prinz Eitel Frederich (t6,) and Scharnhorst (t7.) You could use either of these in operations.
Given a choice I would prefer Graf Spee over PEF at t6, and Scharnhorst at t7, and of these 2 I would go with the Scharnhorst.
TL,DR: on the USN side I would recommend Atlanta if you like to pew-pew HE, or the Boise which is a more well-rounded ship.
On the KM side I would go with the Sharnhorst.