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 on an older laptop with a SATA-1 port and you want 1+ TB, the HDD would appear to be your only choice.
I found the vibration from a 7200 RPM HDD to be extremely fatiguing on my left palm (the HDD was directly underneath it on my old laptop). If I couldn't get a SSD and I had to go back to a HDD, I would instead look for a 7mm 5400 RPM HDD. The 7mm height drives typically use a single platter. 9.5mm uses 2 platters, 12.5mm = 3 platters, 15mm = 4 platters. The fewer platters in the drive, the higher the data density per inch, and the more data the drive can read/write per rotation. So a 7mm 1TB HDD will have 2x the data density of a 9.5mm 1TB HDD, meaning it can read/write roughly 2x as much data per rotation.
This is a bigger speedup than the 33% faster rotation speed of 7200 RPM. i.e. a 5400 RPM 1TB 7mm HDD will have faster sequential read/write speeds than a 7200 RPM 1TB 9.5MM HDD. Your random read/writes are still slower on a 5400 RPM drive though.