Stability is often best using an IOS version that's deep into its maintenance life cycle. One that's in common usage is good too, especially in a similar usage role. The latter can be difficult to determine without, perhaps, contacting Cisco pre-sales.
As a generalization, the larger more expensive devices tend to do well in stability and security attributes.
Sizing a device doesn't much care about host types. What you need to know is aggregate bits per second, packets per second, new flows per second (much, much less important than it once was), how much "state" (e.g. routes, NAT, NetFlow, etc.) information needs to be stored and its "churn" rate.
If you can provide the prior information, router recommendations might be suggested.
