Today there are many NAS devices like this on the market. I guess this depends on the model, but I would like to know if they usually tend to allow you to connect hard drives of different sizes (for example: 1TB, 750 GB and 250 GB) and so I can do a RAID 5 to a limit and otherwise leave it RAID 0.
It depends how you want to setup the disks. If you dont want any redundancy (and the os allows it) you could put disks of different sizes in and concatenate the storage.
If you want to use mirror the disks (raid 1) then you can probably use different size disks but you will only get the total capacity of the smallest disk. If you want to use raid 5 for better redundancy you will have to use the same size of disks.
I would recommend you use the same size/make/model of disks in your device anyway.
Products like the Synology DS409slim and the Drobo FS allow different sized drives to be combined - while still providing redundancy. Synology call this "Synology Hybrid RAID", and the Drobo equivalent is called "BeyondRAID". You can calculate the likely usable space for a Drobo - which is 930GB (with single-disk redundancy) for the drive combination in the question. The disadvantage of these products is their cost.
Regular RAID 5 will be limited by the smallest drive in the array. This is also the case for RAID-Z in ZFS.