Since the person here who is asking for advice is probably on a budget, I think that the calls for him to buy one of each of the early types or a Carson City piece are misplaced.
The St. Gaudens type is readily available in Choice Mint State (MS-64), and might be a nice "starter coin." It was the first coin I bought when I was starting out in 1965. The Liberty type is harder to find nice, and would MUCH HARDER were it not for the 1904, which is a super common date.
If you want to "go exotic" an 1876-S in AU is an affordable alternative. That coin is a type II Liberty which is different on the reverse from the 1904 which is a Type III Liberty.
Here is one I bought many years ago and had slabbed by NGC. Given the ways of "grade-flation" a recently slabbed AU-58 might not look as good these days. This will be harder to find. You can buy a common date St. Gaudens double eagle from many sources.

And here is an 1861, Type I, which I bought years ago. I think that the prices have gone up on these because of the Civil War date, despite the fact that it's a very common date.

Strictly Uncirculated early double eagles are very expensive, but the AU-58s have been a lot more reasonable in price.
Edited to ADD Whatever you do, buy am NGC or PCGS certified example. DO NOT by a raw coin. Getting stuck with a counterfeit is not fun at all and the slab provides you protection from that.
Edited by billjones
02/18/2017 2:46 pm