Hi
If you lump all the opportunities together on a form, and let people know that there is going to be a lottery if you get more volunteers than you need, then it manages expectations and no one feels shut out.
Totally agree with your putting a priority on not turning away (or turning off) parent volunteers.
To me the key is to actively manage the volunteering at school. Do you have a volunteer coordinator position or an involvement committee? I think that's an importnat role for a PTO, especially if you're lucky enough to have an excess of volunteers at times.
Rather than jst saying it will be a lottery, the involvement committee has the job of having right folks in right roles (right butts in right seats) and making sure that new volunteers get utilized and perhaps that new volunteers get teamed up with experienced vets, etc. It's a much more pro-active approach.
The last thing you want come May or June is parents quietly grumbling that :I wanted to help but they didn't take me up on it." That's the quickest way to a clique reputation.
I wouldn't put a cap on the sheet because then you may run into the problem of people thinking "oh, so many other people will volunteer for that event that I won't get called" and they won't check off on the sheet to help with that event. When event time rolls around, you may not have enough volunteers to get the job done without pulling your hair out.
We've decided to try something different this year, and not send out a sign up sheet for the entire year's events. Instead, as the events come up, the chairs will send out an announcement that we need volunteers and to contact them if interested.
In the past, we sent out a sheet and one person would compile all of the information and send lists to each event chair. (I've had the job, hours and HOURS of work involved). The problem we ran into was that some chairs weren't contacting the people on their list first, and would send a flier out asking for volunteers. We got complaints from parents that they signed up to help and no one contacted them, etc. etc. So we're going to try doing away with it for a year and see what happens!