Hi Elisa,
Welcome to the Forum. You cannot go too far wrong with Solarguard paint - no prep or undercoat required and available in a range of colors. If you want you could brush down the wood prior to painting but this is mainly for cosmetic reasons on the finished look. You can use a roller, with a brush for the uneven or hard to get to bits. Put on at least two generous coats and give it an extra slop in any knotholes or imperfections.
If any of the timber has split it has lost its strength and integrity anyway so choosing whether to leave it or try to patch it is mainly a safety and aesthetic issue, not a structural one.