With the recent acquisition of two new pre-33 gold coins at FUN (1908-D No Motto Eagle and 1908 No Motto Double Eagle), the U.S. Gold Type set holes have been reduced to four: No Motto Liberty Head Eagle; and all three Liberty Head Double Eagles. This set does not include pre-1834 coinage but I did succumb last year and bought a 1811 Half Eagle. I haven't decided if I will include an example of either $1 and/or $2.50 Classic Gold Commemorative in the set. Anyway, here in two messages, is the current type set.
The No Motto $10 gold pieces are not too expensive unless you need it in Mint State. Collectors could not afford to set these coins aside in the 19th century. Therefore, unless they are found on shipwrecks, strictly Mint State pieces are rare. I squireled this one away when I was a dealer over 20 years ago. It is an NGC AU-58. The way grading is going these days, this coin would be graded MS-62. The three types of Liberty Head double eagles are challenging in Mint State except for a few dates. Almost all of the nice Mint State Type I double eagles have been recovered from shipwrecks. The 1857-S has became fairly common from the SS Central America site. It's still expensive. Here is a very nice 1861 double eagle I saved from my dealer days. This is one of the more common date. Early in the Civil War, the Union thought that they could back their Demand Notes with gold. They couldn't. The Type II Liberty double eagle is very hard to find in high end Mint State because none of them have been recovered from shipwrecks. This one is graded MS-63. I bought this one raw in the 1980s. It is now in an AU-58 holder. The Type III $20 gold is much more available in Mint State. They get pricey in MS-65. Unfortunately the price of gold bullion is the big driver behind recent price increases. The 1904 is the most common date. This 1907-D double eagle is graded MS-64. You have a lot of the tough gold type coins, unless you get into early gold. That gets wicked expensive, especially for the early quarter eagles.
Didn't forget but both coiled and flowing hair varieties are way too expensive for my middle-class resources plus they weren't ever struck for circulation, if I have that correct.
Yes, the Four Dollar Gold Pieces, also known as "Stellas," are pattern coins that were never made for circulation. I don't think that they are really part of a gold type set. Many collectors don't know this, but some of them were also made copper, aluminum, white metal and gold plated copper. I have seen the gold plated copper pieces offered for sale. The dealer wanted almost $50,000 apiece for them.