Your question states speed is not a factor, but resources are. In this case, HDDs give you far greater GBs for your money than any SSD on the market currently. If you're after pure resource, HDDs would currently be your best option, depending on exactly how much extra resource you feel you need. However, I'm not sure you really mean that, as in the wrong set up, the speed difference could be very significant.
Now, in terms of reliability, that's difficult to say. Firstly, you haven't actually stated what resource intensive operations you plan to operate that may require a swap partition. The swap partition will only be used beyond 4GB of RAM, so unless you're running operations that are consistently causing >4GB RAM to be rewritten, you may not be causing any PE cycles on SSD blocks at all, and these are our usual indicator of how soon an SSD will fail. An HDD will have mechanical factors to take into account. Even reading across an HDD will cause the heads to seek, possibly quite a lot if you're also using the drive as a normal storage device as well as swap memory. This will cause additional wear to the drive.
Secondly, SSDs are a lot more reliable now than they were at their first implementation (Which unfortunately tarred them as unreliable years later), with most of them easily outlasting the normal life of a machine. Again, it's very hard to say exactly how long a device will live (manufacturers will provide MTTF and MTBF averages, but these are on the whole quite misleading and can only give you a vague statistical idea), but one metric that can give you a somewhat better idea is the warranty periods offered, which typically are longer for SSDs than HDDs now (Figured I should cite a source - Samsung provide 36 months minimum for SSDs and 24 months minimum for HDDs).
Let's consider that speed is a factor. Firstly, your motherboard being of an age where it has DDR2 RAM may only have a SATA2 controller, and as such, you'll probably be bottlenecking the maximum throughput of a lot of SSD's anyway. Of course, the main benefit to an SSD is the incredibly low latency and high IOPS against a HDD, which, if you're using it purely as a swap drive, is going to be very important.
Of course, swap is definitely not a replacement for real RAM, and can't come close to matching the speed RAM, even at DDR2 speeds, can reach. An SSD (heck, even a bank of RAID striped SSDs) looks incredibly slow if you're comparing it to RAM. An HDD looks incredibly slow when compared to an SSD. If you must use a swap in order to make up for a lack of RAM, an SSD will at least give you a fighting chance of making up for the drop in speed.
In order of best case scenario in my opinion:
- Upgrading the machine to allow for more, faster RAM.
- Using an SSD as a dedicated swap partition.
- Using an SSD as a shared swap and boot/data partition.
- Using an HDD as a dedicated swap partition.
- Using an HDD as a shared swap and boot/data partition.
If your situation is 2 or 4, the reliability really shouldn't be a concern anyway, as you won't be losing any actual data and the device should have a long enough warranty to cover you until you can go for the best option of actually having more RAM.