Best was to access Thunderbird email from another computer?

Howdy Folks...

Welp, I clicked the T-bird Help section and it brought up this page:
http://www.google.com/custom?cx=003258325049489668794%3Aru2dpahviq8&q=Accessing+email+from+other+computers&sa=Search&cof=AH%3Aleft%3BALC%3A%230000CC%3BBGC%3A%23FFFFFF%3BCX%3AmozillaZine%2520KB%2520%2520Search%3BDIV%3A%23006666%3BFORID%3A1%3BGALT%3A%23006666%3BGFNT%3A%23006666%3BGIMP%3A%23006666%3BL%3Ahttp%3A%2F%2Fwww.mozillazine.org%2Fimage%2FnavHeader.gif%3BLC%3A%230000CC%3BLH%3A36%3BLP%3A1%3BS%3Ahttp%3A%2F%2Fkb.mozillazine.org%2F%3BT%3A%23000000%3BVLC%3A%23499F9F%3B&adkw=AELymgWlIG8H4SvxWMToOixWM7eedE0ArlYGvTKAx4fjOOfI5KUlcrWh7j2y6GxjwHT_uQUvPXZdcCV0-X7vzOLScp-8NOFhSKWSdQKJO96jIi5sNkaSnHXkIxGWYi2Vq_wAs-uiESUm&hl=en&client=pub-0651448570352947&channel=1541744254

Just reading the top of the page tells me I need to download/use some other software (I think?). If so, does any of those look familiar to anyone and can you recommend them? (GoToMyPC, LogMeIn, etc)

Also I noticed in the words written of the other articles I see things like

"You wouldn't be able to access your address books. However, you could export them as..."

and

"There seems to be no spam filter when I use a service like Mail2Web to access my Thunderbird email..."

Am I about to get into something I will regret later? Heck, all I wanted to do on a recent trip I took was check my emails. (Guess that is why I don't give up my Hotmail address, I can get to it from anywhere.)

Any suggestions, please?

Thanks!
Shoe