Step one is again to get onto your hosting control panel and figure out how to backup and restore. Whilst it is perfectly fine to hose several DNN installations at the start the sake of learning (I trashed 9 in a row and have been using the 10th for three years since), you'll soon tire of it. Figuring out how to do it will also lead you on the path towards installing and updating your own fresh copy of DNN.
On to your queries. I don't know where those 'update available' links in DNN go as I disable them, but your best bet is to use the Downloads button at the top of this web page here in front of you. The prerequisites for module updates are listed in the "min DNN Version" column on the downloads page next to each module. There are often minimum versions and the Announcements module required 4.6.2. Not all upgrades are worth it and by no means are all the modules worth it. Reading back through module forums is a great way to find out what matters and what doesn't.
There are several upgrade guides around, Sebastian and Mitchell Sellers have them on their sites - check their signatures.
It sounds to me like you might have tried to update DNN in the same manner as updating a module. This will certainly produce the reult you got there. Updating DNN itself is not nearly as straightforward. It's more along the lines of installing from scratch, but instead, it goes on top of the old version. There are plenty of small details however, so check one of the guides and start digging around your hosting panel to see if you have the necessary tools.
Rob