Check firstly whether it's 3 days or 0.6 spread across four or five. But also check what will be written into the contract - because you don't want to find out the next year that the timetable is totally different, and that your day off is different or non-existent. Watch out for fortnightly timetables, too.
Another thing to find out is whether they manage to timetable you for whole classes or whether you end up with lots of split classes. Being the only teacher of a class is much easier.
Rules can be a bit complicated for part-time. Your proportion is based on the proportion of the teaching timetable you work (including PPA). Your directed time is then based on that proportion. For things like duties, meetings, parents' evenings, you should be doing the correct proportion overall, but it doesn't have to be the correct proportion for each individual thing. If you don't teach all year groups, that usually knocks out the odd parents' evening. I didn't have a tutor group, which cut out some of the meetings. It's best to add up all the meetings/evenings and check whether it goes over - and if so, ask which ones you should skip. For department meetings, the agenda can sometimes be arranged so that you can leave before the end, if there are items which don't affect you.
For training days, if you work whole days, then you do the ones on your days. If that's none of them, so be it; in that case you're probably teaching more days than you should be proportionally. They can pay you to attend extra ones by mutual agreement, but they can't make you attend them. It's a bit more difficult to work out if you work part-days, but in sensible schools you can reach agreement on what to attend - it usually makes more sense to attend a couple of whole days than four part-days.
I worked part-time in 3 different schools, and it worked very well for me. I was unusual in not having childcare to worry about, and I actually preferred to have my timetable split across the week rather than whole days off. I could then fit planning and marking into the gaps and not have school work encroaching on evenings and weekends. This made timetabling much easier and meant I didn't teach split groups, so it suited everybody. Timetabling someone teaching 3 days a week is much harder, particularly in subjects that have 3 or more lessons a week.
The schools I worked in all treated their part-timers well, which meant that there was a bit of give-and-take. If you get a chance to meet another part-timer at interview, sound them out, because I don't think all are quite so good.