The answer is that your going to get side effects regardless of what day you start. If you want to be able to have sex right away, start on the very first day of your period, no matter what day of the week that is.(then when your period winds down, you can have sex without additional protection - or you could even have sex while you have your period)
If you want your period to arrive on Sunday's only, then you start the pill on the very first Sunday AFTER your period starts - the only problem with this is that you need to use extra birth control protection for a full week before the pills are considered to be giving you 100% protection. I myself wanted to start having sex right away without having to wait a week or use a condom, so I started on the same day my period showed up which was a Monday. It really just depends on you - some women like to have a Sunday start because that sort of guarantees them no period on a weekend. The side effects (if your body displays them)will be there regardless of which starting method you use.