To get answers to your specific questions, you are probably going to have to piece together bits of information. Here are a few bits that might help, and a few websites at the end which might prove useful.
The time a journey took would have depended not just on what mode of transport someone could afford but also on the points of departure and arrival. Some places were far more accessible than others - terrain, weather & season, availability of river or coastal transport (often a faster option than travelling by land) and size of the town played a large part in determining the quality of roads and the transport options available. Roads in, near or joining major cities were usually better, but not always:
In London itself the Edgware Road was often deep in sludge, while one irate resident complained that the road from Kensington to Westminster had 'grown so infamously bad that we live here in the same solitude as we would do if stranded on a rock in the middle of the ocean'.
(from Asa Briggs 'A Social History of England')
Carriages weren't just for the rich - they had cheap seats too (a basket on the back or sitting on the roof). The average speed seems to have been around 4 miles per hour. Ox-drawn carts were mostly used to carry goods but perhaps they accepted the odd hitch-hiker too. I'm not sure if your musician would have been able to hire a horse - that would perhaps have depended on how much he was able to earn from his profession.
You mentioned travelling from Milan to Brussels. One option would have been through the Alps which took 5 or 6 days if going via Mont Cenis, depending on the season. This had been a popular route since at least the thirteenth century. Another option would have been going from Milan down to Genoa and then taking a boat to Marseille. Jordan Girardin's PhD thesis Travel in the Alps gives more details on this, as well as options for travelling through the Alps. Once in Marseilles, the (modern) map below gives an idea of how someone might get to Amsterdam largely by River. You can find information on travelling up the Rhone on this Wikipedia page Rhone (History).
As for crossing the channel:
the crossing from Dover to Calais could take anywhere from 3 to 12
hours depending on the wind and waves. A traveler might have to wait
in Dover for a week or more for the wind to be in a direction that
favored crossing the English Channel. In 1772, Dr. Burney, the music
historian, spent nine days waiting for good weather.
(from Grand Tour)
Asa Briggs, ' A Social History of England'
Elizabeth Anne McFarlane, 'French travellers to Scotland, 1780-1830 : an analysis of some travel journals' (PhD Thesis, 2015)
Jordan Girardin, 'Travel in the Alps:The Construction of a Transnational Space Through Digital and Mental Mapping 1750s - 1830s'
Channel Ferries and ferry Ports
Carriages: 17th century
How could you travel across Europe in the 1800s?
18th Century Transportation