You can get a plan here and you have 30 days to decide if you are satisfied.
No host can truly offer "unlimited" resources. Resources cost money, as you have discovered. Choose a host that offers realistic limits for a price you are happy with. You will find that WebHostingBuzz is quite competitive.
As for using too much server resources, that is not only about number of visitors. If you have an insecure or poorly-written script, then it can hog server resources. If that happens here, you will be suspended just like at your current host. If you do not use any scripts, then it may be that your current host is concerned that you are using 1.5GB of disk space. That seems like an awful lot. Here your disk space must be used for web site related files, and not as a file storage. This host also does not allow streaming video or other streamed media.
I suggest you look at the plans here and choose one to suit you.
I am not WHB staff and I am not paid.
I provide help in these forums on my own time.