CONFEDERATION OF THE RHINE
The Rhine is one of the smallest nations in the game.  It has decent troop types and resources, but a small European population.  The Rhine has some holdings, including a mine, in India, and real prospects there.  Unfortunately, the Rhine is bordered by six nations, including Austria, Prussia, and mammoth France.  The Rhine is in a precarious position, but if it can survive the first year its prospects are good. (sample GUI empire file)
 
Economy
The Rhine starts the game with both an ore mine and a gold mine in Europe.  It has a few improved foodstuff, sheep and horse breeding coordinates but overall has limited options for placing production sites such as factories and weaving mills that require high population.  There is also limited mountain terrain for stone-producing quarries.  The Rhine has a single trade city in Europe, Munich, and like Austria has central location that improves the effectiveness of its baggage trains.  Its shipping fleet is large enough to operate in the Caribbean, and Baltic and Mediterranean.  The Rhine has a gold mine and shipyard in Southeast Asia.  This can be developed into a base for Indian trade and expansion.  The Rhine has a fair chance at claiming Haiphong before the larger colonial powers.
The Army
The initial Rhine army is one of the largest in the game: 13 full-strength brigades including 4 heavy artillery, 4 Cuirassier, and 6 Garde de Corps battalions.  The Rhine has an early Simulated Battle advantage.  But, for the most part, the quality of the Rhine's troops is barely average, although its Mounted Artillery has high effectiveness (EF = 8).  The Rhine does have a significant advantage that its infantry have 32 movement points, compared to the normal 28 of other nations. The Rhine's riflemen, though not as effective as some others at EF = 7, is cheaper than most at a cost of 120 louisdore per soldier.  The Rhine also begins the game with full-strength Colonial Troop (Kt) brigade (MARINE-BRIG 2) in Munich, which can be moved and boarded the first turn.  These troops are expensive to maintain, though.
The Navy
A decent sized fleet starts in the European port, and a smaller in the Indian outpost.  The navy totals 12 warships and 566 cannon, including two Class 4 Cruisers.  The battle fleet is not large enough to think of challenging the colonial powers, but is sufficient to maintain a presence in India, and to build upon.
Strategy
The Rhine's only hope depends on diplomatic success.  Strategies include trying to make peace in Europe to focus on India, or forming an early coalition to take out larger neighbor and expand.  The Rhine is typically the target of such an alliance.  Smaller nations like Holland, Denmark and Italy may look towards the Rhine as a reasonable military target.  The Rhine must make preparations for war.  But, if it is too aggressive early, neutral empires may feel threatened and attack while the Rhine is involved in a war on another front.  As an aside, with efficient diplomacy Rhine may be able to acquire the fleets of Prussia, Warsaw, or Austria - and a treaty to boot.
Conclusion
The Rhine is one of the most exciting positions in Austerlitz - so exciting that if you are not careful it could be over before the game reaches 1809.  It is located in the thick of things.  The Rhine is almost always involved in a war the first year, but if it can avoid this, or fight on its own terms, has good prospects for expansion in India.  Playing the Rhine will immediately test your skills as a diplomat and a Simulated Battle general.