This is the first time I will join an ICO... Is it uncommon to invest only a small amount, like 0.25 - 0.5 ETC?
You meant 0.25 - 0.5 BTC right? Doesn't seem like that ICO is accepting ETC.
I'm not gonna tell you if you did the right decision or not by investing in this ICO since hopefully you know what you're doing, but to answer your question: Yes. You pretty much just hand over the bitcoin and wait for the coins/tokens on whatever wallet they're gonna give it in. Make sure to read the ICO page to have full information on how their ICO is gonna work:
https://oxycoin.io/ico.php Looks like their mobile app is still currently in development.
Best of luck.