If your concern was having instruments that are in tune with each other, there are various reasons why some instruments might be hard to get perfectly in tune with each other. Pianos, for example, use stretched tuning due to string inharmonicity. Some tuned percussion instruments might not necessarily be at the concert pitch that you need them to be at: Why is A=442 the common tuning for percussion instruments?
In fact, an instrument might not be exactly in tune with itself! Many instruments used tempered tuning, which is something of a compromise, and many instruments don't really even maintain a steady pitch anyway - e.g. a plucked string will usually decline in frequency slightly as it decays (this can easily be seen on an electronic tuner).
Do instruments even have to be in tune relative to each other in order to make what some people would consider beautiful music?
Not always. The human ear has lots of tolerance for tuning mismatches, and having things sounding perfectly consonant and harmonious is often not what the artist will be aiming for. Some genres such as the blues or gamelan music deliberately use intervals that might not be thought of as the most consonant.
Are some instruments more suited to other instruments, and in what way?
From a sonic perspective, common ensembles are popular because the frequency ranges of the instruments complement each other well. One common pattern is to avoid having lots of different instruments playing different parts together in the same pitch range - and instead to spread parts out across different voices. You can see this in SATB arrangements in a choir, or the use of violin, viola and Cello in a string quartet. The use of equalisation in production allows this practice to be followed even with groups of instruments that wouldn't each fall naturally into different ranges.
For instance, I can't seem to find any examples of certain instrument combinations like a guzheng and a didgeridoo, or 2 triangles a tritone apart, although that's not to say there aren't any.
A lot of common combinations come about because of tradition more than anything else - and also because of practical considerations (e.g. all-acoustic combinations can play together where there's no power; instruments that have similar output volumes work better together, unless you can have many of the quieter instruments; ensembles of portable instruments can be played in more settings).
But that doesn't mean that different combinations won't work. Here's a guzheng and a didgeridoo:
. Does it work to your ears? The didgeridoo seems a bit quiet to me on that video, but perhaps that's just the recording.
A lot of the development in music comes from finding new combinations, rather than things that are essentially original. There are probably many more to be found.