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You want to start out with a skirmish game, and not break your bank. Just get a couple of boxes of your choice of starter set, and a box unit and start from there.

I play Warhammer fantasy, Frostgrave, mordhiem, Necromunda, and a couple of other skirmish that were just a paperwork change, Here is the rules for Age of Sigmar from the website. A small model count, and small play area work wonders to get you into a game. It also gets you inoculated to building these units and miniatures by the batch.
Here are the rules for Age of Sigmar, and Warhammer Fantasy skirmish and Mordhiem.

https://ageofsigmar.com/wp-content/uploads/sites/12/2018/06/AoS_Rules-ENG.pdf

http://the-lost-and-the-damned.664610.n2.nabble.com/Warhammer-Skirmish-Rules-PDFs-td7580478.html

Pros and cons are easy-

PRICE PRICE PRICE- You can get into the game under $25.00- 50.00
Selection- You can use whatever minis from whatever range you want
Rules- Free, or free-ish.

And scenery can be stored in shoeboxes, as you acquire different types, made out of old scrap around the house, some paint, and some sand and sticks.


As to the Navy rules-
You can find something for any era here- http://www.navalwargamessociety.org/rulesonline.html