I'm a newbie working on getting a PPL.
People tell me that if I'm serious about flying, I should seriously
look into purchasing a plane - in the long run it'll be cheaper than
renting.

Here is another viewpoint. Disclaimer: The below assumes you don't have
an endless supply of cash to shell out.

First off, you are a student. Most cannot handle the added distraction
of being a new owner while trying to learn how to fly AND taking ground
school (aside from your day job/school/family). Also, you admitted
yourself you are not sure of what to buy. Get your license and fly a
while in other types of birds. Get a feel for where you want to GO first.

Buying an airplane without losing your shirt (and possibly your life)
takes a bit of experience that you likely don't have. What's the hurry?

Why beat up your bird learning how to land? Beat up the school's plane,
then buy your own.

"Cheaper in the long run" can be elusive. You need to fly a certain
number of hours for the math to work out. Properly cared for airplanes
cost money. Many owners simply run planes out and don't properly
maintain or upgrade them. They live on a shoestring budget and roll the
dice that nothing catastrophic will happen. Some win and some lose. The
winners spout off about how "they did it". The losers say nothing and
quietly lick their wounds. I have said it before. There is plenty of
flying junk out there for sale. You likely cannot tell the difference.
This group tells many tales about deals gone bad.

What if you don't stick it out? The drop out rate for student pilots is
not small. If you quit while owning, you have to sell the beast and that
may take a while (unless you can accept a significant financial loss).

Yes, renting has many drawbacks. Dirty, beat up planes that are
unavailable when the weather is nice. But, they are usually maintained
to some minimum level of safety and they have one great advantage that
you might need right now. If anything goes wrong, you simply hand the
keys to the FBO and say "next". And, like I said, you really don't need
a premium airplane and the distractions of ownership at this point in
your flying.

Opinions vary. Good Luck.
Mike