I currently use HRD, and it seems that one can control it remotely. But can you also listen and transmit? Is the performance any good?
You need something to transport the audio. Skype works okay for voice. Its noise reduction kills CW reception somewhat, not that I ever got CW transmission going

I use SM5VXC's IP sound now. One download link is here:
http://www.wireless.org.uk/remote.htmI have a 60mb/s download at home and 3mb/s upload. How good will this work from a standard hotel type internet connection?
Don't know about that one. It should work okay. I've only done it from work at U of MD to home which is very solid. But it's all pretty small bandwidth stuff.
Can you use a laptop with the built in speakers and mike?
I don't think you'd be too happy with that in the long run if you're going to have actual QSOs. I've dabbled and made a couple of SSB contacts just using my computer speakers at work and the mic on my webcam. But I wasn't being serious about it. Something like an expensive computer telephony headset with mic and headphones might be more like it.
What about firewalls? DO you need to use dynamic DNS?
I had to set the computer to a static IP on the local network and then forward the appropriate ports in my router (one for IP sound and one for HRD) to that IP. I signed up for DynDNS and set my router to update my DynDNS account. But for non-critical things you might just be able to write down your IP address depending on your provider. Mine almost never changes.
You may run into firewalls that you have no control over and that can get complicated. I guess people use VPN software to get around that.