I'm about to take my first Amtrak journey in the US next week. I've heard mostly bad things about it, but it's a third of the price of renting a car, so I'm going for it. I'll be travelling first from EWR to NY Penn Station, then to Albany/Renssalaer, so hopefully it won't be too rough compared to the UK's rail service...
I've done the Penn Station to Albany (and beyond) and back many times. It's usually fairly straight forward, and people actually use it to commute. There aren't the usual delays that sometimes hit Amtrak in other areas. Also, the trains themselves are actually more comfortable than most British trains if a little dated. They were built for long trips. You can get into comfort issues when the train uses freight rails in other areas of the country, but the trip between NY and Albany is pretty smooth. Also, if you were travelling for a longer period, I'd advise an upgrade to business if it is your budget (usually not that much provided it's business and not First). But the short trip you're talking about, it wouldn't be worth it.
Bring a snack or drink if you tend to get hungry because I think they no longer have a snack car on that route. Albany/Ren station is nice. They've built a new station in the past decade or so.
The station you need to try to avoid is Schenectady. We were stuck there for 7 hours waiting for a connection for us to cross the state. It's seedy and there are crazy people who like to hang out there. There's like one room, so you can't escape them. I've done a lot of travel by train, and I have to say that Schenectady is one of the worst "larger" stations I've encountered. I really advise anyone who has a connection through Schenectady to try to change it to Albany/Rensselaer.