Both seem to me (in my inexperienced eye) to be a VG-8, based on not being able to see the clasp or curl well. In VG-8, the 2012 Blue Book has the 1823 at 30 and the 1832 at 28. I don't know what the retail markup would raise it to on either, whether they are particularly tough, or even if the Blue Book is accurate in price. Hopefully someone with more experience in this series as well as pricing will chime in.
I think if you really want that kind of coin, you should put out some feelers here with the longtime members of CT or go check with Lost Dutchman to see if you can be put into one or two of the series in VF-20 or EF-40, as the markup on those (blue book) over the VG-8's is not really extreme. The big jump seems to be between an EF-40 and AU-50. I think in the long run you will find yourself more satisfied, as well as having a better chance of retaining/increasing value and salability over the years.
To "put out some feelers" is simply a way to say you are letting others know you are in the market for the type of coin. Sort of like announcing your "want list" but instead of a want list you are saying you want one or two nice VF20 or better Capped Bust Halves, preferably 1820-36. This enables others to say they will be able to sell you a coin you want. Many people get their collections not by going out and just buying when they see the one they want, but by allowing dealers and others to know to reach out to them when the dealer or other person has a coin you might like to have. Each of those 1820-36 coins of this series (with exceptions of overdates) runs 42 in the 2012 Blue Book (ostensibly dealer's price), and 65 in EF40, with jumps to 150 in AU50. You can also start either looking at Coin Prices mag or other references to get the dealer's costs and what the regular markups are for a coin like this. But without looking at anything else initially, I might presume that a good healthy markup could get a VF coin for about 50 to 65, or a EF coin for about 72 to about 130. That may be right or wrong depending on the availability of the coins in that condition. But if it is wrong, you will find out soon enough, and you still will have started networking for your coins, and if it is right, you will be pleasantly surprised to have a coin you like for a price you can live with down the road. Hope this wasn't overly long for you.
Good example as to why not to rely on Blue Book or Red Book for price guides. The prices in those books were outdated before they were published. Numismedia has the 23 listed at $74 in VG, and the 32 at $67 in VG. eBay has had no completed sales of either date of this half in VG.
BUncirculated, you are exactly right....the moment the book is published it is out of date, whether it is "accurate" still or high or low. It is a starting point, though, and in the absence of other materials and realized auction prices, a person starting collecting can at least start there. I'm not saying that if the price is totally out of wack with reality that the person looking for the coin at a lower price will get it. The ultimate would be to actually "know" your coins, not only with the grading, but also with the pricing. I'm just saying for a newbie who is liking a series, it is a starting point for them.