Step 1) the basics:
The first aim in your game is gaining a second region to become a Great Power, which is necessary since most German minors start off with only 1 province.
But first of all, your finances: Generally education spending can be kept at zero since most German minors start off with +80% literacy, which is more than enough at the beginning. Also I recommend keeping the national stockpile low unless you can recruit new brigades, or when you are at war.
Next step can be done by choice. Especially at the start Capitalists are usually lazy f**k’s who aren’t even building factories when being promoted and low taxed. That’s why I tend to building them myself by switching to the reactionary party right at the start.
Your research should be focused on getting prestige, which is why you should start with Romanticism.
The next really important step is determining your first target to achieve your main goal: Getting a second region to become a Great Power.
Looking at this map you might think that Denmark and the Netherlands are good targets, but I have to disappoint you: You won’t be able to create a CB against Denmark before either Austria or Prussia beat them up, leaving (eventually) only Jylland for you which isn’t worth it since it A) makes your literacy drop and B) gives you a region without any of your accepted culture and not a lot of people in it.
The Netherlands will usually be allied with half of the world before you’ve even halfway created a valid CB against them – in addition to this Great Britain will intervene in most of your wars.
Cutting out those nations there is only one possibility left: Taking a chunk of the Austrian Spherelings Bavaria, Baden and Wurttemberg.
Even though you'll think taking Niederbayern from Bavaria might be the most rewarding goal I have to disappoint you about making it come true. Austria will be allied with them before you’re finished creating a CB. In addition to this achieving ~15 war score against an alliance of Austria and Bavaria only with Prussia by your side is really hard and Prussia is most likely going to white peace out – as long as you don’t occupy all of Bavaria. This leaves Baden, Württemberg and Saxony for you.
This is the perfect moment to check your political screen:
On your question “Why?” there is an easy answer: Some German minors* start off with South German as accepted culture, which might makes Wurttemberg and Baden better objectives for you than Saxony. As you can see Brunswick’s doesn’t have South German as accepted culture, which is why I chose to attack Saxony.
*Hesse-Nassau; Hesse-Darmstadt; Hesse-Kassel; Saxe-Coburg-Gotha; Saxe-Weimar
If either Prussia or you take control over all the provinces of the nation you are fighting it’ll be annexed, making a white peace with Austria possible.