If your arms are your weak link, which is the case for most surfers, rookies and pros alike, then sure, try a harness. It's definitely more enjoyable, because your posture will be more relaxed, making surfing a lot easier on the arms and generally a lot more fun.
Having said that, I'm not sure if the club peeps will let you fit the ropes onto a rental boom though; there are some safety issues associated with a harness after all. But no harm asking eh.
As for the straps/harness order, horses for courses, but I find it easier to strap in after hooking in, because I'm lighter on my feet once the weight transfers to the boom.
Enjoy