I picked up NWS' Rule the Waves (link at bottom), which is a surprisingly engrossing game.
Essentially it places you in the role of Grand Admiral of a navy in 1900, in a world bereft of the alliances. You may choose from 12 historical or 3 alt/hist nations (CSA, for example).
You may choose a historical budget or a larger one for your nation. You are assigned a pre-1900 fleet and a budget, and are set to begin 300 one-month turns.
There are three basic phases to a turn:
You set your training doctrine, intelligence priorities, and research priorities. You may choose to build ships of existing classes, design new classes, upgrade existing ships, build shore batteries, or improve your port facilities (or any combination thereof for which you have the budget funding for), and assign ships to those of the 12 sea regions in which you have an interest.
when you hit 'next turn' you get a screen telling you what news there is, usually just data on who is building or upgrading what, and similar naval related news. Your spies may report, and frequently you get pop-ups advising you of research successes. In additional, very frequently you get a pop-up which describes a situation (enemy spy caught, for example) and two or three different choices as to how to resolve it. Different choices can impact various factors. If you are at war you will get pop-ups with war news.
during a time of war you will get the opportunity to fight sea actions using the tried and true Steam and Iron game system (you do not have to have SAI).
Prestige and Tension:
Prestige is your Grand Admiral's standing within his nation. Let it drop too low and you are sacked, game over. Tension shows your nation's status with other nations. If tension rises too high, war begins. Here is a difficult thing: you will get a political situation arise and have three options: one eases tension but lowers your prestige, one raises both tension and your prestige, and one is unclear. If you sacrifice prestige to keep peace, you can erode your career prospects, but if you go to war and lose, kiss your career goodbye.
Research, or the addiction:
The heart of the game, and the part that is addicting, is fleet maintenance. This is a period of exploding naval technology. Not only will you have to design the actual warships for your fleet, but you will also have to configure the fleet to stay within your budget. Now, there is no 'tech tree' as most games have it; instead there are fifteen or so general areas (Guns, Armor, etc) in which your set your research priority. Nearly every month you will get a popup advising you that your engineers have developed a new armor process (a 1% reduction in armor weight), improved engines (likewise) or something big, like a turret design that can house two guns.
This is where you start white-knuckling it. It takes 20-30 months to build a heavy combat unit, and while you can modify existing ships there are limits to what can be changed. So you designed a lovely ship class, say a pre-dreadnought (B), and then get a dozen or more improvements to your naval tech while it builds. So there is a terrible urge to delay just a turn or two longer in the hopes of getting a pneumatic rammer (increased RoF in main guns) or wing turrets or yet another increase to torpedo range before committing the ship to construction. Of course, that could mean you end up going to war a year later with your hot design still under construction.
Designing a ship is simple in execution and tough in practice. The program handles all the math and has a check feature that warns you if your design is top-heavy or other issues. You have to balance engine capability, armament (size, ammo load, and placement), armor (where and how much), and considerations like crew comfort and range. Not to mention cost, both purchase and maintenance. What sort of war are you envisioning?
I played Austro-Hungary twice after getting down the rules. In both cases I was sacked in 1910. In the first game I did not pay attention to tension, but lucked into an Alliance with the UK, and ended up in a war with France and the US (with the UK as an ally). I did OK because the UK carried the load. The alliance expired and we were drawn into a long war with Italy which we won, but the damage to my prestige was fatal.
The second game chugged along; I fell into a war with Imperial Russia which I won handily. This made me overconfident, and I delayed too long in committing to building capitol ships. My Trung Si
class battleships were sill under construction when war with Italy broke out, and even with modest upgrades my pre-1900 fleet was no match for the Italian vessels which were mostly 1905-08 designs.
120 turns in the above games took a couple hours to play.