Issues with multiple things since Mavericks update

Question

I installed the Mavericks update and since, I have been having multiple problems with different things on my MacBook Pro 13"
1. Printer issues: I have an HP officejet 6500 wireless printer (Officejet 6500 E709n Series), and now it's having major issues with printing, yet was working perfect prior to update. It will either cut out pages when printing PDF documents, or printing so slow that it has to take a break in between printing each document (an issue that all never occurred until update), to print documents back to back, it will stop after one document as though I have no other documents in queue to print, and pauses for an extremely long time (nearly a full minute, no exaggeration here, literally almost a full 60 seconds), something it's never done before this update. My Apps update even did an update to the HP software that is inside the Mac already to use printing (in other words, the mac doesn't need to have the HP software manually installed for it to work, it automatically sees the printer because it is connected to my wireless network just as my Macbook Pro which is also connected wirelessly to my network).
2. Internet issues: am now unable to click on certain links in safari that I was able to use prior to the update, yet they will open fine inside of firefox with no issues, yet I cannot always switch between two different browsers to perform task online (literally have to start all over inside firefox while in the middle of something in safari). Also lots of websites no longer work correctly and I have to constantly clear history and cookies to attempt to use certain sites, at times it will help, other times it wont work period, yet the same exact site will work perfect in firefox (which I do not use, only on my system for use on certain sites for school because in safari prior to the update, I would have issues with only the class site and some links not working at all, no spinning wheel, no errors, just nothing, no response of any kind, basically worse than what it was before the update). Another issue, hit Ctrl+a to select inside Safari and it highlights, but then when you click out of the highlight, it comes back on it's own several times without you hitting anything, just click inside the screen on a blank space (no links, etc) with touchpad.
3. System issues:  My system is way slower than what it was prior to the update, click on things and it wont respond at all, then minutes later will eventually respond or pops up the spinning color wheel, which it either never responds or takes an extremely long time to respond. And no matter how much I restart, it doesn't help anything. Even just to sit doing nothing, no clicking or usage on the system, and the color wheel pops up.
4. Mail issues: Mail is now popping up completely blank messages that I have sent out, the person receives it with no issues, yet I cannot look at the message I sent neither in the inbox or the sent items when I need to look at them again, an issue not present prior to update. Also I an now having issues when receiving mail, sometimes it will check for mail and sometimes I have to manually click to make it check the server for mail, an issue not present prior to update as well.
As of now, since I have had the chance to used the system since the update, these are the issues I have had, yet haven't had the chance to check other things, so there may be other issues that are occurring that I'm not aware of at the moment. I knew it would be a mistake to do this "free" update and did so anyway and now having one issue after the next with each application I open to use.
Mac general info:
Mac is one year old, purchased brand new, no shareware programs of any kind installed.
Use for school and basic web surfing use.
Do not install any programs onto system that I'm unsure are safe (basically programs for/from school/school websites only, or from the Mac Apps store only), not even programs like Skype, nor any windows based programs of any kind.
Lots of free memory avail because I save everything onto external hard drives (purchased brand new as well, only 4months old) in case system crash occurs, only things on the system is Itunes music or pics from photo stream that sync to the system when Iphone connected.
Mac system info:
- Processor  2.5 GHz Intel Core i5
- Memory  4 GB 1600 MHz DDR3
- Graphics  Intel HD Graphics 4000 1024 MB
- Software  OS X 10.9
- Number of Processors:          1
- Total Number of Cores:          2
- L2 Cache (per Core):          256 KB
- L3 Cache:          3 MB

Answer 1

For those needing help fixing their system and putting it back to Lion or Mountain Lion, this is what I have done to eliminate all my issues in about an hour (depending on your internet connection).
Amazing thing, I just restored my computer back to Mountain Lion, and she's working perfect again, as I knew she would. E-mail popping into mailbox instantly as it should and did before the update, printer working fast as it was before update, no more freezing or glitches of any kind thankfully and finally. Here is the link that is through the Apple site to direct you on how to put your system back and get rid of Maverick's, that is assuming that is what you would like to do and also includes link for those wanting to try fixing the issue if that is your preference (most of this info is for those with mountain lion and some with the previousverisoin of OS X lion).
If you want to keep Maverick's here is a good post on the apple discussion board to help you out:
https://discussions.apple.com/docs/DOC-6161
If you just want to totally get rid of it and put back what you had before, this is the short version of how to do so:
https://discussions.apple.com/docs/DOC-3353
NOTE: This particular link has a lot of info on what to do for different situations, it is a bit lengthy, yet still very helpful.
OS X Mountain Lion: Reinstall OS X (direct from Apple support site, not someone else):
http://support.apple.com/kb/PH10763?viewlocale=en_US
OS X: About OS X Recovery (also from apple support directly and includes some instructions just the same as previous links above):
http://support.apple.com/kb/HT4718
Just in case you aren't sure what it will all look like as you are doing things, this is a link to show you a few pics of what you will see  as you as you are going through the process, it can be helpful for those who aren't sure what they are doing or how to do things at all:
http://www.apple.com/osx/recovery/
This is a way to download the Mountain Lion disk info from the server
http://support.apple.com/kb/DL1433
I hope this helps someone, it was amazing for me and my system is working perfect again like it was, battery life is way better went from like 3 hours to like 5 (not on full charge by the way, after it sat for a while doing the online update which took a while so that's saying something alone, huge improvement). I plan to wait a while before attempting to reinstall Maverick's, long enough for them to fix the bugs.