I will try to give you some thoughts to this post and to you post above. These are not necessarily in any particular order.
1) Your move from a hosted account to a virtual dedicated server does involve a learning curve, one whose steepness depends on your own abilities coming into this. I am not an expert at these things, so I typically allow a month to learning these things.
2) What tools are you using: SSH, FTP, the file management system on your VDS? I have found that knowing SSH is very helpful. If you know SSH, I might be able to give you some guidance using it. If not, it can still be done, but it will be a little more difficult.
3) Don't you have a domain? I saw the ip-188.121.. in your file. You will notice in my config.php that it is much simpler with the domain name. Eventually, you will want to use the domain name anyway, so why not start with it.
4) If everything is working well, Moodle will create the config.php file for you. You should not need to touch this file initially. I only edit mine to make a change to ignoring my ssl certificate.
5) I forget, does Plesk have an install routine for Moodle? cPanel does. I don't use these anymore myself. However, you might try it just to see that Plesk can indeed install Moodle for you. It will probably be an earlier version of Moodle (these auto installers tend to lag a bit), but it will probably be version 2.something. Once you have a copy of Moodle working, you can use it as a model for your own install. Or you might keep it and upgrade it to the latest version. I assume on you GoDaddy hosted account, you were using Moodle from the auto-install method.
6) Yes, "moodledata" needs to be outside of hpptdocs, not inside it. Actually, when I had a GoDaddy hosted account and installed Moodle with their one-button install, it put moodledata inside the website directory. I picked up a book on Moodle and learned that it should be outside the web folder, so I moved it myself. On your VDS, the Moodle installer will always suggest its proper place, but you must have "rights" to create it, which you should if you are doing this logged in as the owner of your domain.
7) I am recalling the Plesk did some odd things with group ownerships. I think you want the owner and the group to be the same (in my case, rjerzcom). Plesk seemed to make these different, which is why I might not have had luck with it. cPanel kept these the same.
8) There is a video somewhere of a person showing how to install Moodle. I saw it once, thought it was pretty good, but I can't remember where. It might be on YouTube.
9) I took note of your "video" needs. I also recall that you have a small site. I make extensive use of videos in my courses, but I do not have a streaming video server. Here is an example of what I am doing to deliver my videos to students. If you play a video, as long as you are on a DSL or better Internet connection, the video should stream for you. I am using a very low cost solution. I don't know if any of this is of interest to you, but I thought that I would mention it to you. Below are two different approaches.
9a) Click here to view a single video from your browser, it should stream.
9b) Click here to view my current course videos, from my video player. Try clicking the "All" button, you might be surprised to see all my videos. Here is one more example that you should enjoy (Slightly outdated, however. Making this current is my winter break project.)
10) Relative to videos, you can also find my course videos on iTunes. I podcast these, and I also use Moodle's RSS feature to provide another way for students to access these. All my videos are now MP4s, not FLVs. I used to do FLV but no longer need to. Again, I do not use a streaming server to deliver these.
Well, I have given you probably more information that you expected. Maybe my numbered list will make it easier to address any specific thing that I said. It appears that Ken, Howard, and maybe some other folks are also doing a good job helping you.
If you are enjoying some of this, you probably have the right mentality to be successful. If all of this seems to be a big pain in the butt, you might have to consider other approaches (such as letting TMDHosting, or some other company host your Moodle).