Hi,

**Based upon this sketchy info, would I be better off to buy a new
washing machine, or is there a good chance that a visit by a repairman
would be sufficient and cost effective?**

Fix it if not over 50% of the cost to replace with a new one....your
washer was made to last 20+ years easy!

**What would a "house call" by a repairman cost me, ballpark figure?**

Will vary from place to place....but most are approx $40-80.00

**Could this be a loose belt of some sort that I could either tighten
or replace myself?**

Loose, probably not....something seized or jammed up is possible and
the belt is now jammed and burning as it tries to go. Maybe a sock in
the drain pump or such.
http://www.applianceaid.com/maytagwash.html

These machines for the most part are easy to work on
jeff.
Appliance Repair Aid
http://www.applianceaid.com/