It is alright for me to be house hunting, or am I going about this too fast? Should I get an apartment instead?

You have no income to buy a house.

You are too big for your britches.

Dorm it.

You also have no income to live in an apartment either.

At 18, with (presumably) no decent income, credit score, or deposit of at least 10% of a property value, buying a property is not going to be an option. 

You rent what you can afford. 

There's a time and a place for home ownership.  This is not that time:

1) Even if you own a home you still have neighbours.  

2) 'Some' apartments will allow you to have a pet (with restrictions typically weight-based); a small cat is fine.

3) Even renting an apartment will require a credit check and a deposit (typically, you pay first and last month's rent along with a security deposit).

4) Owning a home means if anything breaks, it's on you to fix it.  Apartments are different- they will have someone fix things if something breaks.

5) Owning a home means you own it.  If the housing market goes to crap you're stuck with it, whereas with an apartment you leave when your lease is up (or you renew).

I really think you need to grow up about 5-10 years more before attempting to buy a house, since you have none of the requirements. Ditto for an apartment. You need money, and credit for either one, and you have neither. Slow down. You're jumping the gun here. 

Neither.  Rent a house.  You can't afford to buy one, and you want more freedom and privacy than an apartment would give you.

you may not qualify for anything.

To be considered for a mortgage you have to be employed,  need to put a down payment of 20% of the asking price and still have at least 1/4 of the price of the house in your savings account.  At age 18 you probably don't qualify,  even for a WHEDA loan. 

You can't get a mortgage on a house, and would need roommates to rent one.  Best idea is a year or two in dorms, then rent a house or apartment if you can afford it.

Not to put a damper on things, but unless your parents are going to foot the bill for your house, there isn't a reputable bank that is going to give you any kind of money towards a house. You have to be able to show proof that you can pay the money back over the next 30ish years with or without a job. Even looking at apartments I doubt you will find a place that will take you in. You had better plan on staying with your parents, getting a job or an education, get some money in the bank and then worry about moving out on your own.

The question is written as if you have a choice. Credit rating over 550 and stable to improving, down payment no less than a few percent plus closing costs, two years continuous employment, low side debts. PITIH Principal plus Interest plus Property Taxes plus Home Insurance plus HOA not to exceed 32% of gross income and maximum 39% for debt load including PITIH.

18 means hardly a credit score.

You can look at what homes cost online. You can research what the monthly numbers are.

One loan Amortization web site

http://www.bretwhissel.net/amortization/amortize.h...

You can't even rent an apartment without cosigning parent(s) with a good credit history.

You don't even know what to do with your life.

You don't mention a job and career.

The question is only full of info as to why you can't rent or buy.