It's funny cause many of what others have said they don't use, I LOVE and use all the time!
Stroller - LOVE IT! We go for walks daily in it. I have a baby carrier as well but she's getting so heavy that it hurt my back. I WISH that there were prams in Canada...
Baby Monitor - again, love it! It's been a huge lifesaver as we moved K to her own room at 6 weeks and it gives us peace of mind that she's ok as it has a movement sensor on it.
Baby bath - K loves this and I find it so much easier to leave it on the bathroom counter and fill it using a juice container. Ours has a little drain with a plug so it's easy to empty when we're finished.
Change pad - I really like having a change pad in her room where everything is set up and i can take her change her. We also have one that comes with our pack and play so if we're downstairs we can change her too.
Don't buy a really busy play mat....babies are amused with small and simple things. K loved to look at faces on stuffed animals and other items too for hours when she was younger.
Oh and if you're breastfeeding, I love my breastfeeding pillow, especially when I feed her in the glider. It really saves your arms!
Good luck - in the end you just have to choose what you want...everyone is different and uses things differently. My hubby and I are outdoorsy people and thus we got a stroller that could go with us when we go hiking etc.....