>> I guarantee that when it does, I'll try to pump it up and find that I've got a pinch puncture like what happened on the first attempt today.
I changed a tyre for the first time yesterday. I watched a number of videos on youtube first to see how it was done.
They said you could avoid pinch punctures by slightly inflating the tube first (just enough to give it some shape) and then pushing it up in to the tyre before putting it on the rim.
It worked for me. Unfortunately I twisted the chain and spent ages trying to untwist it but that's another story!
I always inflate the tube slightly, makes it so much easier to fit when it has proper shape. Also, once it's all together and before inflating properly, push the valve into tyre nearly all the way through, then pull back out, I think this prevents the pinch flat near the valve at least (read that somewhere), then secure the valve if it has a lock ring and inflate.
Also, before inflating I will push the sidewalls inwards and look between tyre and rim all the way around, just to check if any tube protruding through.
I have some of those pedro levers - nice and strong but I find them difficult to get under the tyre in the first place to remove, and once the first one is locked in place next to impossible to get the second one in.