....The Bach lute suites fantasizes me the most but I am still greedy about playing Dowland, too.
Having read over discussions, advices from luthiers and lutenists institutions, it appears to me that it would nearly be a default for beginners to start with a 6- or 7-course Renaissance lute as they would be appropriate for Dowland pieces. However, they have often remarked that there would be nothing wrong to start with a Baroque lute if the Baroque suites attracted you the most. But I do get an impression that Baroque lutes are not meant for beginners. Some even mentioned that not to think of playing Dowland pieces on a lute with 10 or more courses, and these two kinds of lutes seem to be largely "incompatible" with each other. Is it just going to be a lot easier to start with a Renaissance lute? Comments appreciated.
The Bach lute suites don't really work any better on the Baroque lute than they do on guitar except one can play the full range of notes. So they wouldn't be my first motivating factor in getting a Baroque lute. However, there is a huge repertoire for the instrument, written by lute players, which is well worth getting one for.
There are two main configurations of the baroque lute, 11 course and 13 course. The 11 is often considered a bit of a transitional instrument which covers much of the French and some of the German (Early Weiss etc) with the 13 course considered the culmination of the instrument...not quite, there were other configurations but this is an acceptable generalization.
The 6 -7 course lute does cover the majority of the Renaissance repertoire, including much of Dowland. However, Dowland did write for up to 10 courses, as did many others and there is great late renaissance/Early baroque Italian repertoire which requires a 10+ course instrument. It's a bit of a purists myth that the earlier repertoire of Da Milano through Dowland cannot be played on 10 course lutes. It is a similar myth to the guitarist one that states, don't even think about playing the 19th century repertoire or renaissance lute music on a modern guitar. You can play what ever you like on what ever you like as long as the understanding is that the experience is not what the original player and listeners would have had.
As a side note on lute tunings, the Italians didn't adopt the D minor tuning during the Baroque period but maintained the renaissance tuning and extended the range by adding more bass strings.
The main issue with switching from guitar to lute, especially Baroque lute, is that the task of dealing with a larger number of strings/courses can be formidable. This seems to be why the recommendation from most lutenists is to start with a 6 or 7 course, maybe an 8, move on to 10 and then transition to the Baroque tunings with the 11 or 13 course. By the time you get the 13 course Baroque lute you have a fine stable of instruments with which to cover the entire repertoire.