I have older macs 10.5.8 osx. my computers at home and my new phone cant get emails. its says cannot connect to server

Question

Like I said I have older macs but a new phone and I know longer can get emails. It says cannot connect to the server

Answer 1

Get more information about your computer. Go to the Apple in the upper left corner of any window, then  "About This Mac".  Write down what it says about "version"and report that here.  Now continue to "More Info..."  Copy and paste the information here, but omit the serial number and Hardware UUID (if present).
Check system requirements:
Snow Leopard 10.6 Technical Requirements - http://support.apple.com/kb/SP575
The main issue might be having too little RAM.  Most computers run newer systems more smoothly with more RAM than Apple says is a "minimum" for running that system version
After installing 10.6.3 run the updater to 10.6.8, then upgrade iTunes.
Jan. 2014 post by Kappy on doing all this: https://discussions.apple.com/message/24599931
The new system should install on top of the old one.  That said, things have been known to go wrong and it makes sense to do a backup before installing the new system.  In fact you seem to care about your files and things so you need to always have a backup because one day you will wake up and you hard drive will be dead and everrything on it gone.  Buy an external hard drive and start using Time Machine or something to back up. The other risk is when you install the new iTunes.  It doesn't happen frequently given the millions of users but there are daily posts here from people who for some reason the installation wiped out their whole library.  If you have a backup then there's nothing to worry about. 
This is well within what many people can do at home.  It's a matter of inserting an optical disc and clicking you way through menus.