i am trying replace my worn out battery and am not sure what physical size i can get.

The easy bit is that it is 175mm wide (that seems pretty standard and should fit) and it could be up to 300mm long - most batteries are either far too long to fit this or are significantly less (e.g. 260mm long).

The issue i have is the height. When i got the car, there was nothing fixing the battery in place.
Do i need to purchase the top ( part no 577020 which is 305mm long 180mm wide) and the 4 J bolts (562953) to hold it in place, or is there an alternative method?
If i do purchase these, it looks like the J Bolts limit the height to around 190m - my old battery was 180mm high so i guess it would fit, but that limits the batteries i could buy?

The yuasa batteries good and Tanya deliver at a good price too
Currently trying to get my rebuilt 2286 diesel going in the garage

Battery mega store deliver free, prices often the same

I have a ratchet strap holding my battery in. I think it was a Wilko one. Small but not completely cheepo junk. It’s been on (well greased) for years and passed several MOTs without comment.
I have a Bosch battery (out of a Audi A5) in the heap and although the first one was well used I was impressed enough to replace it with a new one last year.

Something like this for holding the battery down is ideal.