I should prefix this by saying that I wear hockey skates, not figures. That said, I agree with TSV. Yes you can get high end boots from the word go, but you might lose interest in skating, or you might decide you want to pursue a different style of skating. A new hockey skater would do okay to spend up to £100 on a pair of basic but decent skates to learn in. They should last 6 months if the person works hard, much longer otherwise, before they need to upgrade. Of course someone could take the risk and go for posh skates instead, and in that case they MUST make sure they fit properly. Go to a good shop with a wide range of skates. That also applies to cheap skates, but the financial risk is less of course. I don't know where you live, and I don't know about figure skates, so someone else will need to make suggestions of where to buy.
In my own case I had a pair of cheap Bauer hockey skates for 15 years. When I upgraded, the plum at Guildford rink who sold them to me did not know what he was doing, so the new pair did not fit, and I had to spend another £200 on some that did fit. Oddly enough the two skates felt totally different, so I suspect there was something wrong with the first pair I bought, maybe they were worn out or something.