For free launching in Christchurch, the quay is the the best slipway.
Mudeford is near the sea (benefitting the tidal issue, saving about 20 mins depending if you abide to speed limits 😉
but they charge for the privilege.
Poole is a much larger harbour, hence the no tide issues but for a first time boat user Christchurch is much more small boat friendly, and as there are two highs every 12 hours if you plan your time and choose your days this is no major issue.