Assuming you go down the square taper route (as this will be by far the cheapest option):
No matter what bits of kit you end up plumping for, pick your chainset first. This will determine the axle length required (check via Google etc.).
(As any quick Google will tell you, there are many different BB axle lengths available. This is to ensure that the chainset is placed in the correct position relative to the frame, thus ensuring the correct chainline.)
The 68mm/73mm dimension refers to the width of the BB shell. Simply measure the BB part of the frame. 99% of frames will be 68mm (give or take a couple of mm).
As regards English vs Italian BBs, both types have a right-hand thread (i.e. tightens clockwise) for the left-hand cup. Italian BBs also have a right-hand thread for the right-hand cup. English BBs have a left-hand thread (i.e. tightens anti-clockwise) for the right-hand cup.
It will most likely be cheaper to get your LBS to source and fit the BB (compared to cost of BB, P&P, fitting tool).
As regards the type of square taper BB, wot workers_united said:
"In addition to the British/Italian threads types, there are two types of square BB tapers - JIS (as used by Shimano) and ISO (as used by Campagnolo). Although the BBs and cranks can appear to be mixed, they won't fit properly so it's safest to fit BBs and cranks from the same manufacturer unless you know that they meet the same standard."