Cloakroom Renovation & S Trap Toilets

[FoleyKaptain]

Hi everyone,
I’ve recently purchased a 1970’s house and am trying to be more hands on when it comes to renovation and general improvements. We got a professional to do our upstairs bathroom but I’d like to try and tackle the downstairs one as the stakes don’t seem quite so high if I mess up (no water pouring through the ceiling and way less plumbing).
Part of the work required me to remove the S Trap toilet so I can screed, tile the floor and do the skirting. I’ll be replacing like for like as I managed to save the cistern so will just get a duplicate toilet basin.
I’ve got as far as removing the old plastic waste section that joins the ceramic basin waste to the clay (?) pipe in the ground and now I’m a little unsure of what to replace this with. So far I’ve come up with the following…

https://www.screwfix.com/p/mcalpine-push-fit-single-socket-drain-connector-black-110mm/4255V?gclsrc=aw.ds&gad_source=1&gad_campaignid=19822796606&gbraid=0AAAAAD8IdPzrhqLP_5oVy3DF_Yhdqj4Xo&gclid=Cj0KCQiAr5nKBhCpARIsACa_NiNhHYZJTvbuVOmh30yaU1xBwmze3PQyMps__BFa0CZsAsKnbSruqEAaAruWEALw_wcB

….but I’m not sure exactly how this connects in and if any other parts are needed. I’ve included a few photos of the hole (sorry, it was a lot worse before I’d cleaned it). I think it measures 4” in diameter. Any help would be fantastic, thanks!
Keith