Personally I like owning over renting. Renting has its purpose - if you need to remain mobile, in case you get a job offer that requires you to move to a different city/state/country - if you rent, it'll be easier to move. If you owned, you have to deal with selling your property which is more challenging when you are not in the area.
Another reason to rent is if you get a really sweet deal on your rental, where your payment is less than that of a house payment, you can use the low rent to your advantage to save up extra money so when you are ready to buy, you have a nice down payment.
If you are starting up a business, renting may be for you as well - as most of your focus will be on getting the business going, you probably wouldn't have the time to focus on house maintenance. Renting where you have a good landlord that takes care of things like cutting grass, snow shoveling, indoor maintenance - works to your advantage to free up your time.
Eventually if you get settled in an area you want to stay, or if the cost of renting doesn't provide any savings advantages, the best bet it to own. That way you get to keep most (and if you are lucky maybe make a little extra) on your investment in the house when you do sell it someday.
Between a house and a mobile home - from a resale value, I'd choose the house over the mobile home - mobile home values don't hold up very well, generally speaking. I also like having the benefit of a basement that houses in my area have (mainly because of tornado safety reasons).