I see that UVDan mentioned,

My internet connection is DSL which needs the phone line from the telephone
company.  So I would be calling over my computer over the phone line.

True. 

OTOH, although I don't have DSL, I understand that with DSL you would have both high speed internet (RJ-45 wired, wireless, or USB ... depending on the DSL modem) and also an analog telephone line (RJ-11).  The calling plan on the analog line (RJ-11) determines you usage cost for local, long distance and international calls. 

The reason you might want to use an alternative service is that your long distance or international calling costs might be lower than what your telephone company would charge for usage.  In addition, with Skype, you also get 2-way video. 

Some monthly cost comparisons ...

$44.00 Telephone company (unlimited US and Canada) +tax

$25.00 Vonage (unlimited US) +tax

$2.95 SkypeOut (US)
$9.95 SkypeOut (Global to 34 countries)
$3.00 SkypeIn (provides an incoming telephone number)

If any of this is unclear, please ask. 

Any other comments ... please. 

--
Martin