There are no grammar schools in Croydon, but girls go to Wallington Girls in Sutton and Newstead Woods in Bromley. Both are "superselective" grammar schools. Several children each year go to the grammar schools from Park Hill, though typically these children will also have had private tuition from Year 4 or 5.
Rather than trying to plan the entire educational route for a 2 year old I would start by looking at what is around you and taking it one step at a time, especially as you might move at some point over the next few years.
Looking at state options, Park Hill is considered to be one of the more "academic" primary schools. It does give quite a lot of homework from early on. St Peters in South Croydon also has excellent results. Despite its name it is not a church school. If moving were an option then most Croydon parents favour the Sanderstead schools (Ridgeway, Gresham, Atwood), unless they have the Catholic option in Purley.
To say that Old Palace is going downhill is possibly an exaggeration. However both Old Palace and Croydon High have had challenges in holding onto their best girls in 6th form for various reasons, but that is some way off. Also neither school will prepare your daughter for the 11+ exams as they will want her to go through to their own senior school. You would still have to tutor if you wanted a different school then.
Oakwood (a catholic school) and St Davids in Purley both prepare for 11+ and are both co-ed. Both seem to be good schools with happy pupils, also slightly cheaper than the girls-only alternatives (though I don't know the fees for the Cumnor House school yet). And obviously Cumnor has taken over the former Lodge school. I suspect that they will give quite a lot of attention to the school as they look to make their reputation, and obviously it is the academic results which count.
You want "good facilities". Can you be more specific about what you're looking for? Obviously a junior school attached to a senior school would have these (and of course Old Palace junior is on the former Croham Hurst senior school site, so has amazing facilities for a primary school).
In terms of getting into senior schools it is much harder to get into one of the grammar schools at 11 than it is to get into Old Palace or Croydon High. Typically it is considered that if you can get into a grammar school then you would be scholarship material at one of the independent schools.
Go look at the schools, get a feel for the head. There isn't one school out there which is the "best", you need to consider which one will be best for your child, which is only something that you can work out as your child develops more.