You could use sem which is part of GNU parallel.
0 0 * * * root sem --jobs 1 --id MyQueue mysql -xxxxxx -pyyyyyyyyyyv -hlocalhost -e "call MyFunction1"
1 0 * * * root sem --jobs 1 --id MyQueue wget -N http://mywebsite.net/path/AfterMyFunction1.php
This cron config will first start the mysql through sem, which will put it in a kind of queue called MyQueue. This queue will probably be empty, so the mysql is executed immediately. A minute later, the cron will start another sem which will put the wget in the same queue. With --jobs 1, sem is instructed to execute only one job at a time in that particular queue. As soon as the mysql has finished, the second sem will run the wget command. sem has plenty of options to control the queueing behaviour. For example, if you add --semaphoretimeout -60, a waiting job will simply die after 60 seconds.
The && solution is probably better, since it won't execute the second command when the first one fails. The sem solution has the advantage that you can specify different cron settings, like a different user. And it will prevent overlapping cron jobs, if the cron interval is shorter than the job duration.