Welcome to the forum!
That's a pretty good lineup you're considering. Your question about which Adams is kinda complex, actually.
There are 3 models of Adams euphonium, not counting the marching horn: E1, E2, E3. Within each of those are some options (as you experienced with the horn that had a sterling silver bell). ALL of them share some characteristics: excellent intonation (the best of any horn I have played), easy response from note to note and in various ranges, and hand-made construction using sheet metal for better resonance.
E1: The original model. It is considered a good all-around choice and is easy to play. The sound is not as large as the E3 but it is a tad easier to control for a less experienced player. It is also the best choice for small ensembles, chamber, and solo/piano playing because the sound is a bit more focused. The sound "sings" very nicely. It might be more comparable to the Prestige 2051.
E2: I think this might have been made to appeal to Willson players. It is heavier with some bracing differences, which gives it a very good "core" to the tone. The sound is powerful, but not quite as open as the E1 or E3.
E3: This has a more open throat in the bell and creates a larger sound. It would be more aligned with the Prestige 2052. The sound is very open and sings well. It responds as easily as the other models, but can require more work to get the most out of it. Interestingly, I found it easier to play on things that required a delicate touch!
The biggest option is the type of metal. The Selected models use yellow brass. This is what most horns use and is a good choice if you don't have a chance to sample others. It will sound nice as soon as you play it. You can also choose other brass alloys, which vary the amount of copper in the mix. Gold brass has a bit more copper and has a bit more "zing" to the sound. Red brass has the most copper and I find it to have a warm, dark sound.
Metal thickness is another option with the E1 & E3 (I think the E2 comes with only one thickness: .80). The selected models use .60, which is a nice compromise. It balances its characteristics nicely. The .70 and .80 choices are less common and have a bit more power capability as you add thickness. In theory, lighter metal has a bit quicker response and a bit lighter sound. The lightest I would suggest is .55 if you really favor easy response and a lighter sound - but you would not have as much volume capability.
Sterling silver is a special case and is only used in the bell, and more recently is an option for the leadpipe. It has the greatest range of tone for an experienced player to leverage. It is capable of great projection and sounds ranging from very dark to quite bright. It also adds a lot of cost!
Mix & match will create more fine tuning if you have the luxury of trying a bunch of them. At the 2012 ITEC in Austria I had a chance to try one in .50 metal with a red brass bell. The bell helped give it more power and authority than the .50 would otherwise have, but the .50 metal made it VERY friendly to the player. That is just an example for an extreme illustration - I would not suggest it.
When in doubt, get the selected model. It is less expensive and a good balance. If you want to ultimate in performance options, go with the sterling bell.
As I was considering going to the E3, and then later as I was considering going with heavier brass instead of the sterling bell, I did A/B comparison videos. Perhaps they will help you see some of the differences I'm talking about. You need to listed with good speakers or headphones. And you may come away thinking, "Gee, there is hardly any difference." As a performer, I want a horn that lets me sound like me, so my basic style and tone concept will be there with the A or B choices. But there are differences to be heard "at the edges."
If you like the sterling sound but don't want to spend the extra $1k+ for it, that second video shows an interesting option. Going to heavier metal helps get you much of the benefit with no price premium.
E1 vs E3:
https://youtu.be/7Uc_Ag0bYiE
E3 sterling .60 vs. E3 .70 yellow:
https://youtu.be/DlM1lC6moKw
#adamscomparisons