It takes a standard 2.5" parallel ATA-6 drive. You're looking at about $60 to $80 shipped for a replacement. R32's aren't so old that they have small disk size limits, and you should be able to go beyond 137GB as long as you have an NT or Linux based OS.
Here are a few options that would probably be best for that notebook:
Western Digital WD400BEVE 40GB 5400MB 8MB - $46.99
Newegg.com - Western Digital Scorpio WD400BEVE 40GB 5400 RPM 8MB Cache ATA-6 Notebook Hard Drive - OEM
Toshiba MK6034GAX 60GB 5400RPM 8MB - $50.99
Newegg.com - TOSHIBA HDD2D17 (MK6034GAX) 60GB 5400 RPM 8MB Cache ATA-6 Notebook Hard Drive - OEM
Seagate ST980815A 80GB 5400RPM 8MB - $58.00
Newegg.com - Seagate Momentus 5400.3 ST980815A 80GB 5400 RPM 8MB Cache ATA-6 Notebook Hard Drive - OEM
Hitachi HTS721060G9AT00 60GB 7200RPM 8MB - $66.99
Newegg.com - HITACHI Travelstar 7K100 HTS721060G9AT00 (0A25022) 60GB 7200 RPM 8MB Cache ATA-6 Notebook Hard Drive - OEM
The general rule in laptops is your hard drive is typically the bottleneck. Older laptops usually came with 4200RPM drives, which were very sluggish. An upgrade to 5400RPM will result in a nice performance boost, but a 7200RPM would be even better. It's up to you if you think it's necessary and a good value. But it certainly couldn't hurt (7200RPM has a minimal impact on battery life and heat generation, probably the biggest thing you will notice is noise however since it's spinning at desktop-speed). Anyway, on to installation:
This should be very easy to do. Remove the drive bay cover (might have to loosen a screw), grab the plastic tab, give it a good yank, and your drive caddy will come right out. Then you unmount your old drive from the caddy (4 screws usually) and remove the adapter if it's equipped with one. Then just reverse the process, mounting the drive to the caddy (reusing old screws if the new drive doesn't come with them), pushing in the new drive (adding the adapter from the old drive if necessary beforehand), and then securing on the bay cover. Shouldn't take more than 5 minutes (it's in fact easier than replacing a desktop drive IMO).