SATA III is backward compatible with SATA II or SATA I ... just like USB

It is the other way around. The SSD with SATA II itself is backward compatible. If your laptop is SATA I, the the SSD with SATA II will perform like SATA I SDD 

I don't know what you meant by this. I guess you confused.

IDE (Integrated Drive Electronics) was the original name, then they standardized on ATA (Advanced Technology Attachment) as being a broader standard that included additions like CD-ROMs and such. When SATA ( Serial ATA ) came out, people started using PATA (Parallel ATA) to refer to the older parallel connected bus (those using ribbon cable), to be more specific than the term ATA, which can refer to either. Both are part of the ATA standard, and use the same logical command sets, but SATA obviously has a different electrical interface. Both types of drives (SATA and PATA) are IDE devices.

I think there is no more old IDE (PATA) hardisk in market. My old laptop at home no more hardisk for replacement. Buy used one maybe is the only choice. for desktop PC, you can buy adapter to convert to PATA but laptop has no space for that.

So, most likely all new HDD has SATA III interface support but since your laptop is SATA I, so you will get the SATA I performance. Therefore, if you can find the SATA I hDD out there, it would be likely cheaper than the one that support the SATA III 

Whatever SATA version your laptop have, when you installed SSD to it...the responsive of system is much much better than all HDD out there...