"Will i have any problems just transferring exactly what's on my shared hosting to what i'll have if I purchase a vps here"
That is a loaded question.
There is not a button that you press and everything swooshes over to your new VPS.
You must do some set up work first, then make sure your original files and databases are all backed up and safe, then move those files and databases over to your VPS, then move your domains to your VPS.
If you have some idea of what you are doing, or are willing to be patient and read tutorials and ask questions... then you should be able to transfer everything to your VPS and have it working within a few days at the most. Usually sooner..
Once you get everything moved, you will end up with your own server that is very fast and inexpensive that you have complete control over.
If you get frustrated easily, do not have the time to deal with it, or are too nervous about the process, you might do better with a hosting account somewhere that has good technical support.