If you are to upgrade in the future, it is far better not to have to change all of your accessories, so consider this when purchasing now. That means No.2 Morse tapers, and care in choosing your chuck, when you come to buy one - see below.
As stated by others M33 x 3.5mm is a standard spindle size for larger lathes, but at least one of the lathes you listed has a 1" x 8tpi thread - which is pretty much standard for small lathes made in China and sold under many different names here. Either would serve you well but remember that any chucks or faceplates you buy have to have a corresponding thread.
For chucks, this is usually done by changing an insert, but sometimes chucks have to be direct threaded to suit the larger sizes such as M33. For example, a Record Power SC4 chuck takes inserts up to and including M33 so it is simple and cheap (abt £15 - £20) to upgrade from a smaller thread to M33. The Robert Sorby Patriot chuck, on the other hand, cannot accept an M33 insert so you would have to use a £40 excert - clumsy and expensive. I don't know about the Axminster chucks.
Keep away from No.1 Morse tapers unless you get a particularly good deal on a Record lathe; virtually everything nowadays uses No.2 Morse tapers so your spur drives and centres would work on pretty much any lathe that you bought.
On a slightly different note, variable speed is indeed worth holding out for, but be aware that some are much more variable than others. Three main types:
Mechanical - have a selection of speeds, accessed only whilst the lathe is running. The mechanism typically needs to be cleaned annually to keep it sweet (straightforward).
Electronic, 3 phase - the best. May well vary speed from around 50rpm up to 3000rpm. Usually rather expensive.
Electronic, dc - found on the cheaper lathes such as the Axi you listed. Very convenient in use, not so torquey as 3 phase, typically offer 450rpm to 3000rpm. The carbon brushes on the motor will need replacing at some point - ask the shop how often. At least one lathe user manual I saw recently said renew every 50 hours! Probably a typo, but may be as well to check (your suggested Axi lathe manual doesn't even mention them).
Better still, buy a nice 2nd hand variable speed lathe, typically 1/2 to 2/3 of the new price and may include some tools, chucks etc. There will no doubt be some coming up for sale around Christmas time as some lucky blighters upgrade!
Good luck,
Duncan