How to punctuate a direct question at the end of a sentence?

The most common and most traditional is arguably this:

Based on your experience, which type of paint do you suggest we use: glossy or matte?

In principle, the colon could be replaced by a comma or even a dash, but I am going to argue that the colon works best here.

Discussion

The comma before which

The comma preceding which is not controversial; see the many results here.

The supplement glossy or matte

Also not controversial is that glossy or matte is a supplement, i.e. a part of the sentence that is not integrated into the syntactic structure of the clause, but is instead semantically linked to an anchor. In this case, the supplement has a form of an appendage. In general, supplements that are appendages should be either put into parentheses, or else preceded with one of the following punctuation marks: a comma, a colon, or an appropriate form of a dash. American usage prefers an em-dash without spaces around it, while

in British usage, an en dash (with space before and after) is usually preferred to the em dash as punctuation in running text, a practice that is followed by some non-British publications as well. (The Chicago Manual of Style (17th ed.), 6.83).

According to CGEL (p. 1350),

In speech, supplements are marked as such by the prosody: they are intonationally separate fromthe rest of the sentence.

The comma is the 'lightest' separator, so it will correspond to the shortest prosodic break in speech.

Parentheses not appropriate

It is non-controversial that in your case, using the parentheses would not be appropriate.

Em-dash disfavored

I would say that the em-dash would normally be disfavored here. According to The Chicago Manual of Style (CMoS),

Em dashes are used to set off an amplifying or explanatory element and in that sense can function as an alternative to parentheses, commas, or a colon—especially when an abrupt break in thought is called for.

Note that introducing a list of items is not specifically named in CMoS as one of the functions of the em-dash. In your case, glossy or matte is more like a list of items.

Where CMoS does mention em-dashes is with expressions introduced by that is, namely, for example, and the like:

There are simple alternatives to the stigmatized plastic shopping bag—namely, reusable cloth bags and foldable carts.

Best bet: the colon

On the other hand, CMoS says the following about the colon:

A colon introduces an element or a series of elements illustrating or amplifying what has preceded the colon.

Grammarbook says this:

Use the colon after a complete sentence to introduce a list of items when introductory words such as namely, for example, or that is do not apply or are not appropriate.

Examples:

You may be required to bring many items: sleeping bags, pans, and warm clothing.

A colon usually does not precede a list unless it follows a complete sentence.

Note that, in your case, what precedes the appendage is indeed a complete sentence: Based on your experience, which type of paint do you suggest we use?

The comma: a possibility

Finally, let's discuss the possibility of a comma.

I looked through all the uses of comma described in CMoS, and the closest ones are those where they separate descriptive phrases (e.g. That was John, with a hat all crooked), possibly with introductory phrases like such as and including.

Having said that, to my ear, using a comma to introduce glossy or matte introduces a level of lightness, of informality (which would explain why CMoS, a very academic style manual, would not recommend it for this purpose). In speech, it would correspond to a shorter prosodic pause than the colon. This effect might be appropriate, depending on what you are trying to accomplish with this sentence, and of course depending on the context.