A lot of them made by several makers and several countries. There can be a lot of history in any one rifle. They were in service from around 1907 through the 1950's in the Commonwealth and later in other countries.
Looking for matching bolt receiver and barrel is a good start. Then the sight base and sight, nose cap etc. Nice wood is good, but not always collectible if that's what you are after. Most original furniture sets if you can find a rifle with one has its bruises and dings from many years in the field and on the parade square.
A rifle produced during the Great War years always appeal to me(1914-18). For your first rifle, any of the desporterized rifles that are matching and put back together with new "old stock" wood, a nice sling and maibe a bayonet and scabbard,... makes a very nice looking rifle and some not bad shooters with good to excellent bores at around 500 dollars. I wouldn't throw too much money at the first one, it will give you something to look over, fondle, shoot and and familiarize yourself with the No1 without breaking the bank, and then after lots of research on here and in print, you can start moving on to more desirable in the collectors department if you so chose, but be careful may turn into a bottomless pit lol.
On my meager budget and other firearms interest's I've accepted the fact that just filling the widely used variants of the Lee-Enfields, not merely your SMLE's or No1's,..... from the Great War(WW1) onwards with one solid representation,is about as much as I could do. No1MkIII, No1MkIII*, No4Mk1, No4Mk1*, No4MkII, No5Mk1, and so on and so forth.
It takes much money and passion to start filling up many safes with many different years and variations from the same manufacturer for instance. I'm sure there are collectors on this board with my two tin cans filled with No1's alone, I envy but realize it's not for me without a lotto win or a miracle.