How to replace carpet with tile in entryway
It's not clear whether you'd like to keep the hard floor after your friend departs, but you might consider vinyl plank flooring. It would be much quicker and simpler and can be quite beautiful. You'd simply remove the carpet, install 1/4&quot; underlayment plywood, and stick down the vinyl.
Modern vinyl plank flooring is quite durable and attractive. Don't let the name make you think it'll look cheap.  Select a product that's self-sealing at the joints. You can cut it with a knife (straight single cuts) or a jigsaw (curved or compound cuts) and it doesn't require grouting.
If you do want to use ceramic or porcelain tile you'll probably need to add at least 1/2&quot; to your subfloor. You need a minimum of 1-1/4&quot; to prevent cracking of grout joints and the tile itself.
Also, I'd consider a full rectangle. You'll find that your carpet suffers less wear and soiling if you have enough room to enter and remove footwear before making contact. This is a common strategy in snowy climates. You could also do a clipped corner if it protrudes into your space too far. That would still be easier than cutting curves and fitting your carpeting to it.