How do I fix super slow internet - all browsers are affected

Question

There is some problem with internet connectivity with my MacBook Pro, but I cannot figure out how to resolve it.  Speedtest.net is measuring my internet speed at download speeds of 0.88MBps and upload of .84Mbps.  Other devices utilizing the same router also via wifi (my husband's MacBook Pro for example) are running at 4.08MBps down and 0.86MBps up.
I've tried many things, but I must be missing something and do not understand what is causing the problem.  Please let me know what I need to do to resolved this.
Symptoms are occurring across multiple browsers (see list below), and I also tried the iTunes store and it was also extremely slow to load.
Safari 7.1.3
Chrome Version 40.0.2214.111 (64-bit)
Firefox 34.0.5
and iTunes 12.xx
Mail program also exhibits a lack of getting and downloading new email that I know if should download, because it shows up on our iPhone.  Attachments in Mail have also sometimes been blank with zero bytes, but if I restart Mail, sometimes those attachment then have data in them. 
The Mail problem seems to be possibly intermittent, but the internet browser speed is really a significant and consistent problem.
I have:
Restarted our router.  (no improvement)
Verified permissions.  (no improvement)
Repaired permissions. (no improvement)
Verified disk (it's okay). (no improvement)
Safari>Preferences>Privacy>Remove All Website Data.  (no improvement)
Safari>Advanced>Stop plug-ins to save power changed to "unchecked" (no improvement)
Reset Safari (no improvement)
Quit and Restarted Safari
Firefox>History>Clear History (Browsing&Download, Cookies, Cache, Active Logins)
Quit and Restarted Firefox
Chrome>Clear browsing data
Quit and Restarted Chrome
Restarted the computer multiple times. (no improvements)
Shut down computer, System Management Controller - SMC and Reset P-RAM.  After restarting after this last bit, speedtest.net clocked in a 4MBps when I first launched Safari, but 2 minutes later, it was slow again at 0.93MBps.
System Preferences>Network
Wi-Fi is "Connected"
In "Advanced" -
Wi-Fi: my Network Name is at the top of the list.  "Remember networks which computer has joined" is checked.
TCP/IP: Configure IPv4 "Using DHCP"
DNS Servers: 192.168.1.254 Search Domains: Home.  There is only one in the list.
Proxies: No boxes checked.  "Bypass proxy setting for these Hosts & Domains: "*.local, 169.254/16"  "Use Passive FTP Mode (PASV)" is Checked.
Hardware: Configure: Automatically.
Please let me know any thoughts on troubleshooting and thanks!
15" MacBook Pro 2.8 GHz, late 2009 model running OS 10.9.5.  Software Update - everything is up to date.  Including the Security Update 2015-001.  Internet was slow before this last update as well.

Answer 1

Safari is not the only browser that's slow.  Will Safari slow down other browsers even if Safari is not running?  Right now I'm using Chrome after restarting and it remains very slow.
Nonetheless, in Safari:
In "Top Sites" of a new tab, I held down the Option key and clicked the "x" for every single top site so that the list is empty.  No change noticed.  I also emptied the folder for cache website previews in the library folder, but that has made no noticeable change after restarting.
What do you mean by "sharing your devices?" Do you mean a network?  I don't have any podcasts, I don't know what you mean by this?  I also don't understand refreshing automatically?  I'm not running iTunes right now.
I have taken a screen shot of Activity Monitor after restarting and this is what shows for CPU.  What data specifically are you looking to analyze in Activity Monitor?