It has been interesting reading everyone's opinions on this! Thank you all for your advice.
I take your points about rotary cutters being quite dangerous on their own, and with the mats, quite expensive.
And also, that weights might not even be necessary with a few handy bits nearby. Or you could make your own (such a good idea
@Fajita )
I also realise that pins are probably going to be the best thing to secure fabric for making clothes, so I'd never be able to avoid them entirely.
I was able to buy a magnetic pin dish at our sewing shop (thanks
@Ploshkin ) and some flat head flower pins (as used by @Bogwoppit ), so these should help keep them easy to find and all in one place. As she also said, I'll just have to be careful to not leave them on the table and always put them back in the dish.
I'm going to see how I do with just those for now, and invest in the cutter and mat in the future (given that we've just had the big outlay of the machine). They do look impressively quick, from the videos I've seen on YouTube.