Your options are actually very limited if you want to do all that with one box, unfortunately. There are only a handful of manufacturers left still making Blu-ray players - essentially LG, Sony and Panasonic - and of those, I think only Panasonic still make models that record to disk.
Their Blu-ray/HDD Freeview recorder has been around for nearly 5 years now. It was
well-reviewed at the time but
it's still expensive, even 5 years on. The
last firmware update was Feb 2019 and it's doubtful it'll get many more updates (if any), so it might be missing certain apps or features you'd get on a newer PVR. I can't say I'd recommend spending so much on such an old machine, but it does look like it'll do everything you want though.
If you decided you didn't need the Blu-ray recording capabilities, then there's a
cheaper option that records to DVD, but a 500GB HDD is pretty small in the age of Freeview HD. Depends on how many recordings you like to store up, I guess.
DVD Freeview recorders used to be all the rage a long time ago, but many people moved on to the convenience of PVRs which did away with the hassle and expense of continually burning disks. In turn, the rise of the streaming services has lead to a reduced demand for PVRs, although many people - including myself - still use them and they are still currently made by manufacturers like Panasonic, Humax and Manhattan. If you decided you wanted to record Freeview and keep your disk player separate, then the latest
Humax Aura 4K PVR might be a good option to look into as it's a very recent model and one of the best-specced PVRs around.
I guess you just have to ask yourself - how often, in the age of catch-up TV services, you think you'd want to burn anything you record from Freeview onto a disk ? If it is something you think you'll make use of and you wanted a one-box solution, then I think your choice may just be limited to the two Panasonic models I mentioned above.
