Passed my tech exam last week - what's a good first thing to try on the air?

That paperwork line about using an old call only applies to people who held a license before and let it lapse. Since you've never been licensed, it doesn't cover you. You'll need to wait untill your call sign actually shows up in the FCC database before you key up. In practice mine took about two business days, and most folks report the same, but it can stretch to a week or so depending on how fast your exam session gets filed. Search your name in the universal licensing system once a day and you'll catch it the moment it posts. The call sign you figured out from the sequential numbering system is ussually very close to what you actually get, sometimes exact.

On the repeater question, it's not weird at all. Announcing that you're new and listening is one of the most normal things you can do, and hams generally love a fresh license. A few things first, though. A lot of repeaters on those club listings are dead or have moved, so listen for a while and see if you hear anyone, or at least catch the repeater identifying itself. If it's been silent for days, it might be offline and no amount of keying up will fix that. Once you've got your call, just key up during a lull and say something like 'this is [your call], new technician, just listening and saying hello.' Use your call sign when you start and when you finish. Somebody will almost always answer, and if they don't, try a diferent repeater or different time of day. Evenings and weekend mornings tend to be busier. Also worth checking if that local club runs a weekly net. Nets are perfect for a first transmission beacuse there's a set structure and people expect new folks to check in. If you tell us your general area, someone here can probaly point you at active repeaters and club schedules.

Seconding the net suggestion, that's exactly how I made my first contact years back. My club ran a Tuesday night net and I just checked in as a visitor, and half the roster stuck around afterward to answer my dumb questions. Also congrats on the one shot pass, that evening only studying paid off.

Gotta push back on the idea that somebody will almost always answer your first call. Maybe that's true in a big metro, but out here the main machine goes weeks without a peakeep and my first few hails got dead air. Didn't mean anyone was ignoring me, there just wasn't anyone listening. So if you key up a few times and get nothing, don't take it personal or assume you broke a rule. Try a different time slot, find the club's Sunday net, or check if there's a second repeater in the next county that actually gets traffic. The radio sitting silent says more about local activity than about you.

One thing that bit me with a radio that sat in a drawer for years: double check the programming before you transmit. Mine had the wrong offset and a tone code copied off some website, so I was hitting a repeater that never heard me. Listened fine, got nothing back, thought the machine was dead. Re-did the channels off the club's actual info page and it worked first try. Also toss the old battery pack on the charger the night before, those things self discharge sitting around.