Common font choices for (La)TeX documents w/ math see e.g. http://www.tug.org/mactex/fonts/LaTeX_Preamble-Font_Choices.html. If you don't want to go through the process of preparing fonts for use with (La)TeX yourself (or perhaps having to change your workflow to some newer TeX derivate that accepts system fonts), see http://www.tug.dk/FontCatalogue/ for a quite a few examples. For my PhD thesis (not in math, but anyway) I used a combination of Gill Sans and MT Joanna, using fontinst and a few other things to prepare the fonts for pdfLaTeX, but this was a conscious choice related to the subject - although noone got the joke in the end…

I've seen the font catalogue, wasn't impressed with anything there. By the way, I feel that the euler math typeface is really really ugly! I don't understand why so many people seem to like it. Anyway, my current favourite for serif is MVB Verdigris. What might be a good sans to match it? And will it work well with any existing math fonts?

Btw, thanks for the first link.

Euler was a design by Zapf and when paired with Palatino is actually quite pleasant. It resembles a mathematicians' hand writing to some degree. However I would not consider it for any publication except for self-amusement.

There are a few faces combinations I use for type setting math papers. Some of them are old type one fonts, others are available as both type one to work with all major TeX engines, or opentype math font to work with LuaTeX and XeTeX using Unicode-math. For text font I always prefer fontspec + opentype.

For math fonts, the most important aspect is it's spacing, optical sizing, and accent placement, and weights etc. A symbol that looks out of place because of pure kerning or an accent looks misplaced, or a bold symbols looks imposing rather than merely important is catastrophic no matter how pleasing the design is.

1) Minion Pro + Minion Math (PS, OT). Yes, too many people use Minion to the point that it feels boring. However, this is the only serious high quality humanist math font out there. The rest of the list are either technically inferior (like those old PS fonts) or unpleasant design-wise (like those paired with times (new) roman). It lacks calligraphy capitals and blackletters. I usually take the ones from Neo Euler (OT math version of Euler) for these.
2) Palatino + PA math (PS). There are numerous math fonts that claims compatibility with the venerable Palatino. But PA math from micro-press is the only one I would consider to be even close to harmony when paired with Palatino. Unfortunately there's no face out there pair with Aldus very well, which I prefer a lot to Palatino for text.
3) Times new roman + MathTime Pro II (PS). Again, numerous math fonts claim to be times-compatible. MTPro two has the best spacing/optical sizing so far. More recent additions are STIX and its derivative XITS. Both are OT. Version two of STIX has opentype math support, but there are some wired accent placing issues when used with LuaTeX. Probably an engine bug that's going to be fixed in the next release later this year. Times is the kind of face that has no personality at all. You can't get too wrong with it when setting a math document, neither can you go very far.
4) Cambria Math (OT) + whatever Text face that matches its weight and width. It has by far the most complete set of symbols. 7000+ glyphs vs. 2000-4000 in most OT math fonts. It's spacing and optical sizing are decent. Unfortunately, it's ugly, especially when printed. However, when paring with a slightly darker face than Minion, or one that's more sturdy, I usually resort to Cambria if there's not too much math in it,

There are a couple of oddities in Cambria Math, but it indeed has the largest set of math symbols I know. I use it paired with Minion, but only for those symbols.

Yan, Cambria Math's OpenType math extensions only work inside Microsoft Word. Are there appropriate LaTeX bindings for it as well, or do you have to use it as any 'regular' font (albeit with an extensive character set)?

John,

LuaTeX and XeTeX have had OpenType math support for a long time. Check out http://ctan.org/pkg/unicode-math, by the same author of fontspec.

I mainly use LuaTeX. At the moment there's some small spacing issues with LuaTeX with some OpenType math fonts, but fixed in 1.0 release, which will be included in TeXLive 2017 later this year.