My current bike has a triple - it was popular at the time especially on bikes marketed at women.
I’m not wedded to the idea of replacing it with another triple - especially as they are a bit harder to come by as they have fallen out of fashion.
Can a triple be replaced with something else? And still have low enough gears to get my lazy @rse up big hills? I think I’m in need of a bit more technical know how.
You can still get triples, Shimano Tiagra has a triple option, and yes you can replace with a double, but clearly then its new shifters time too, and ideally a chainset compatible with existing bottom bracket (although a new BB is quite cheap and easy to fit, especially if you have a threaded BB)
If you are going on the refurb option, what groupset have you got on it at the moment? this is most important bit of info for accurate advice on how to upgrade it / replace bits.
You may not need a whole new groupset, but your issue is if say you have an old 105 10 speed, the new Tiagra 4700 10spd isn't compatible with it.
Also when you say worn out, if shifters and derailleurs are working then new cassette chain and chainrings could breed a lot of life into it for not a lot of outlay. the shifters are the most expensive bit of the group-set.
I'm assuming on 12 yr old Jamis road bike its rim brakes?
re getting low gears on a double, with the right rear derailleur you can run such as 11-34 cassette at the back which will give you a "1-1" lowest gear with a 50-34 compact chainset. you can get even bigger rear sprockets. there are options to go lower with gravel group sets, but these are pretty much then all for hydraulic disc brakes... thee are getting less options new for rim brakes, which is a shame.
the other option is a decent 2nd hand groupset off
ebay from someone who has upgraded to Di2 or similar.