Any 2.5" SATA drive will fit the SATA interface.
2.5" drives come in a variety of heights (thicknesses), with 9.5mm being the most common. There are also 7mm, 12.5mm, and 15mm. Most older laptop HDD bays can take up to 12.5mm, but if your laptop was designed specifically to use 9.5mm or 7mm, the larger height drives may not fit.
On an old laptop like yours 1TB should not be a problem. Be careful going beyond 2TB though, as some older BIOSes have a problem addressing a drive that large.
Be aware that while 7200 RPM is slightly faster (7200 / 5400 = 33% faster), it can cause a lot more vibration and noise (varies with each individual drive). I normally recommend people get a SSD instead if they want speed. However, since you're...