What is best way to allow a user to start an ad hoc job?

I think I might have answered my own question. When I added the SQLAgentOperatorRole to the user in question I was able to start the job with that user. Now I just need to make sure that this is a secure choice.

The operator role will let them run all jobs, you only want them to run one, so go for less permissions as @Magnus has mentioned

Actually, we are looking to give the user access to more than one job. Instead of going down the route of creating a stored procedure for every job, which is doable, are there any concerns of give the user the SQLAgentUserRole role and then give them ownership of the jobs?

If you want the user to be able to alter own jobs, create new jobs etc then SQLAgentUserRole would fit.

The stored procedure I suggested can easily be altered to take the Job Name as a parameter, have execute granted for everyone, and have it check against a table that you create, which jobs the current user has permission to run. Like this.

CREATE TABLE JobRunners (ID int identity(1,1) PRIMARY KEY, JobName nvarchar(100), loginname nvarchar(100))

CREATE PROC RunJob(@MyJobName nvarchar(100))
WITH EXECUTE AS 'loginname'
AS
IF EXISTS(SELECT * FROM JobRunners WHERE JobName=@MyJobName and loginname=SYSTEM_USER)
BEGIN
    exec sp_start_job @job_name = @MyJobName
END

I would prefer doing that rather than giving the user permissions to the actual job, but that's because I wouldn't ever want to have "my" users creating jobs on their own.

A job can only have one owner, but with "my" solution, more than one user can be allowed execute permissions.

Of course, I should have realized that you could just pass in the job_name. This is exactly what I was looking for, and I like restricting the user by using the WITH EXECUTE AS instead of giving them access to the role.