The easiest way is to copy an existing design. Either print a page from a "free manuscript paper" website and measure it, or get some good free notation software (e.g. MuseScore) and see what defaults they use.
Traditionally, all the spacing was relative to the spacing between adjacent staff lines (not the size of the complete staff!)
For paper that is about A4 or USA letter size, the usual standard is 12 staves per page, because 12 divides nicely by 2, 3, 4, or 6 for small ensembles.
For scores with more staves, the paper size is often doubled (A3 or USA tabloid) and traditionally the staves were custom-ruled to match the instrumentation being used. Special pens were made to draw all five lines of each staff at the same time, with consistent spacing.
The "standard sizes" for these staff-ruling pens (in points - 72 points = 1 inch exactly, taken from the setup options of a professional-standard music engraving app) were
Rastral Space between Size of
Size staff lines 5-line staff
0 6.52 26.08
1 5.60 22.40
2 5.24 20.96
3 4.96 19.84
4 4.61 18.44
5 4.25 17.00
6 3.90 15.60
7 3.40 13.60
8 2.62 10.48
A common default size for computer software is staff size = 7.00 mm which corresponds exactly to rastral size 3.
Some instruments often have leger lines below the staff, others mainly above, there should be a bigger vertical gap between groups of instruments (wind, brass, percussion, keyboards, strings, etc), some percussion instruments (or groups of instruments played by one person) don't need five lines buy only 1, 2, or 3, etc ... far too many options for "general purpose" MS paper for a big orchestral score, where you can't afford to waste space on the page. Of course computer software doesn't require any pre-planning of this sort of thing - though the lack of planning can lead also to a lack of thinking about the design of the layout, which is a bad thing!
For standard combinations like solo voice + piano, a pre-printed layout with the appropriate spacing for each system of three staves is useful, and can work "better" than 12 equally spaced staves per page. Again look at what the professionals do!
I don't have access to orchestral sheet music, though.
There is a huge collection of orchestra scores (many with the parts also) downloadable free from http://imslp.org/ - and lots of other types of music besides. Look at 19th-century hand-engraved scores and parts, as beautiful examples of how to pack the maximum amount of music on a page and keep it readable - but you will often find the spacing between staves varies from staff to staff and is different on each page, which is not practical for pre-printed MS paper.
IMSLP also has facsimiles of manuscript scores, particular of earlier compositions - so if you want to see exactly how "MS paper" was designed in Bach's or Mozart's day, you can find out for yourself. (Warning - some of it is not a pretty sight!)
Note, for orchestral parts, the other issue apart from the staff size is the paper size - A4 or US letter are both a bit small and narrow. On the other hand the upper limit to the size is what will fit on a music stand without causing "accidents" when turning pages, and (for opera or theater music) the height is limited by what will fit under the lamp on the music stand, since the auditorium and orchestra pit are blacked out during the performance. 9x12 is common, 10x13 is about the biggest practical size. If you exclude the page margins (which can be the same in both cases,) a 9x13 page gives almost twice the "useable area" per page than US letter, and therefore the music can be laid out with better page-turns more easily.
I'm not entirely convinced by the recommendations of "minimum 8.5mm" for orchestral parts - unless this is specifically talking about hand-copied scores, which tend to be less neat and tidy than engraved and printed ones (whether hand-engraved or computer-engraved). For engraved scores, 7.0mm is usually quite readable. Don't forget that the professionals who hand-copied music for a living were often paid by the page, so they had their own reason to make the staves as large as possible!
For some instruments (e.g. organ music) scores are traditionally in landscape format not portrait - again, the reason is to fit on a music rest that is relatively high for the performer when the instrument has several (e.g. 3, 4, or 5) keyboards - and old pipe organ consoles usually had the music stand "inset" within the case of the instrument, so no extra vertical space was available!