The type of hobby saw depends upon what you want to do with it.
For straight cuts, I use a razor saw with mitre box. The advantage to using the mitre box is that it's easy to setup a jig so that you can repeat cuts of the same length very quickly. You can get the saw & mitre as a kit
from Amazon.com for about $12.
For curved or round cuts, use a coping saw. These can be picked up in almost any hardware store for $5 - $20 depending upon quality.
If you want to go all out, get a scroll saw. This is essentially a powered coping saw. They are expensive, ranging from $100 on the low end to over $500 on the high end. They are a tool for woodworkers, and can also be purchased at hardware stores.