The D600 uses a PATA connector, not a SATA connector, which all modern SSDs use. There were a very few PATA SSDs in the early days but they were wickedly expensive, had a very low write cycle rating and were not very fast.
The machine is also a first generation Centrino Banias, running at 1.4 GHz on mains power, dropping to 500 MHz on battery, if the battery still works, so even if you found a solution, I'm not sure it would do you much good.
The USB ports are 2.0, so a portable SSD won't help much, you need a 3.0 to make sense.
Depending on why you want to replace the HDD, if it's for performance, you would be much better off with a newer machine, even a refurb, which you can get with a warranty of 3-12 months. If you go down that route, a factory refurb is better than an independent in most cases. Or if you are more adventurous and you know what you are doing, you could try an auction. The machine I'm using now, I bought ex-lease 4 years old for $39 Australian. It will take an SSD. It came with a wiped hard drive but the CoA was still attached, so I used that key to install Win7, upgraded to Win10 on the free upgrade, runs just fine, though for my use, I have it running OpenSUSE Leap 42.2 Linux (yes, I'm cheapskate!). What's not to like?
If you just want to increase your storage capacity, you will find it extremely difficult to source a PATA drive these days. I did manage to source a Samsung Spinrite a couple of years ago at 160 GB but it was a long exercise searching.
You could always look at using an external drive if you just want capacity, not performance; there are lots of 32 GB USB 2.0 thumb drives around, which will almost double your capacity.
The D600 was a nice solid machine in its day but I fear it is coming to the end of the line, unless it's still useful in its present configuration. It will run Windows 7 or 8.0 (why would you!) but nothing later, the processor is hardware deficient. It would run Linux quite well, if you want a challenge and you choose the right distro!