While backups are certainly a good idea a better idea are:
- read the TOS/AUP before you sign up.
- remember you get what you pay for.
If the host is offering you everything including the kitchen sink for next to nothing consider that your website may not fit their business model. Obviously they wish to attract websites that consume little or no resources. Which makes sense when you're offering 1TB of disk space and bandwidth for 5.99 per month lol
If you read their TOS/AUP and find numerous terms regulating resource consumption then you know this is not the host for you. Especially when the terms suggest micro management may be their forethought.