In my experience clubs are: a) going to tell you what you want to hear when responding to your questions (“Our pace of play is great!” “If you have guests we’ll make sure you can get them out here.”) regardless of how true that is and/or b) the membership person you’re talking to may not know the ins and outs of the golf side of the club and thus won’t know the truth with golf-specific questions (I’ve found this to be more true at corporate owned clubs and/or clubs with multiple amenities with membership directors not focused solely on golf.).
I’d also consider how and when you like to play and make sure the club’s operations are consistent with your goals. A cautionary tale: the first club I joined was a large, corporate-owned, very social club that had all sorts of golf outings during the week. This would be great except for the fact that I typically try to play 1-2 quick rounds after work during the week by myself and these events made that impossible. One week there were twelve events on the four days the club was open during the work week - rendering my membership useless.
Long story short - grab a copy of the club calendar and make sure how the club operates is consistent with what you want out of a club and don’t necessarily rely on what the membership person tells you.
Similarly, grab a copy of the bylaws/club rules/etc. and understand the rules and restrictions, especially those for junior members, for yourself. Next, if possible, pick the brain of an existing member that will shoot straight with you so you can get real answers to your golf-specific questions such as pace of play, how strict the club actually is with junior member rules, etc. as in my experience as long as people in the golf shop like you and you’re not unreasonable they’ll be willing to work with you.
Probably goes without saying - but play the course and seriously think about whether you’ll be happy only playing one course for the foreseeable future.
Ask for a summary of all fees that will be charged, including service fees on all purchases, tipping policy, assessment policy (if any for junior members), food minimums, cart fees, locker fees, monthly “newsletter charges”, staff holiday bonuses, etc. and factor that in to your budget.
Another random piece of advice based on experience - make sure they haven’t just sold two holes of the golf course and the practice area to a neighboring hospital in exchange for the hospital promising not to develop the property in the next couple of years and then failing to tell you about it when joining the club. In all seriousness - be sure to ask whether there are any projects coming up soon - would suck to join and then two months later have the course redo its greens for four months or something like that.