Thanks for your question and welcome to the community.
The most popular style of carpet sold today, texture, is great for really any home including yours. It's the style that is plush but durable. It's the type where you see the 'track' marks once you vacuum the area.
In terms of what type to buy, consider buying Lifeproof carpet. It's the best warranty and quality carpet The Home Depot sells today.
Click here to read more about it. Once you read the article, you'll also see the padding we sell for it as well, at least the best version to use.
Your carpet and pad can be ordered at your local Home Depot through a flooring specialist. Be sure to see if your mobile home is eligible for installation. If it is not, you will still need to get accurate measurements for each room in your home to get the right amount of carpet and pad.
Let us know if you have any further questions,