Alternatives are permitted in claims. One way is just with the word "or". Another way is via a so-called Markush group. "and fastened with at least one item from the group including screw, nail, glue, and, rivet . . .".
One worry about alternatives is alternatives on top of alternatives and other limitations in a claim that might pertain to some alternatives but not to others.
Yes, you can use means + function to include everything clearly stated as a structure to achieve the means that is set forth in the application-as-filed, and equivalents within the meaning set forth in case law. M+F claims have their own history of judicial interpretation. I would us M+F in parallel with other claims of similar scope that did recite structure.
If structure is actually required - the limitation that thing1 is securely attached to thing2 with location X mated to location Y might be all you want to say. A lot of "ors" in not mentioning the "means" at all.
The caveat is good claims that hold up, are hard to design around, and say what you think they say are very hard to draft.
From a law firm article about or, and, and or/and -
Another example shows the importance of carefully choosing alternative language when drafting claims. In Kustom Signals, Inc. v. Applied Concepts, Inc.,5 Kustom Signals added the limitation “selecting either a greatest magnitude or highest frequency search” to the claim during prosecution and later sued Applied Concepts for patent infringement. But Applied Concept’s device searched both magnitude and frequency. The Federal Circuit reasoned that “or” is not “and/or” and the claim only covered a choice between either one of two alternatives, not both. The Court then affirmed a ruling of noninfringement by Applied Concept’s device. The outcome was indeed unfortunate for Kustom Signal, but it could have avoided the problem by carefully drafting the claim to read, for example, “selecting at least one of a greatest magnitude search and a highest frequency search.”
If this holds, using both some screws and some glue is not infringed by "screws or glue".
A suggested library -
Essentials of Patent Claim Drafting
Rules of Patent Drafting: Guidelines from Federal Circuit Case Law; 2017
Landis on Mechanics of Patent Claim Drafting
And keeping up with developments in the courts and at the USPTO via blogs, PatentlyO, for example.