Hi Sarah, and Welcome to WikiTree!
Geography (and the political history that keep changing it) is not my strong suit, but I have been learning a lot about Germany in the 1800's and early 1900's lately, since I took on the role of coordinator of the Holocaust project, so perhaps I can be of some help.
First, WikiTree has a massive category structure that I find very helpful to get the place names right. For geographical categories the top level is Regions and that page is at
http://www.wkitree.com/wiki/Category:Regions
From there, you'll see a list of subcategories that include two of interest to you - one named Europe and the other named Europe (en). There is a parallel category structure for the English names of places in Europe (that's the "en" one) and the native language names of the same places.
When you are writing the narrative, you want to use the English names, but in the data section you want to use the native language names.
To continue ... if you click on Europe (without the en) then you'll see a list of the subcategories for all the countries, including one for former countries. You will also see a line across the top with the names of languages and you can click on the word Europa under German to get to all the countries for which German is the native language. There, you can click on Deutschland (that's German for "Germany").
You have finally reached a page that will be very useful to you. Notice that there are 2 subcategories that include the word "Baden" ... so, Baden was not a separate country, but was part of Germany. If you can figure out which one is the right one for the place for the profile you're working on then click that ... if you get to the end of the subcategories, you will see links to profiles there (Baden is the lowest level subcategory). If you see names of localities there (Baden-Württemberg has more subcategories) you can select the right one.
You can add the following on the top line of the biography:
[[Category: Baden]]
and that will add a link to the Category page on the profile, plus a link to the profile will appear on the Category page.
The way I determine the correct place for the time period I'm interested in is to go to wikipedia and look up the place name. There should be enough historical information there to figure out what country the place was in at that time.
Please feel free to contact me privately if I can be of any further help to you.
Good Luck!!!