DISCLAIMER: if you don’t have experience with some of the more midrange and budget gear, I would highly suggest you consider trying that stuff out first, imo it’s very valuable to try out some of the more budget stuff to really start to understand your preferences first. It can be very valuable to really start from the lower end and climb to the higher end, you really nail down what you are looking for and also understand what you are getting for your money. Also the journey and experience is really fun, it’s no fun to start near the top lol. It’s very hard to confidently say what you want without having heard examples of it, so I do think it really is smarter to start lower end here if you are new to this (it will be more rewarding in the long run imo). If you have already tried some of the more midrange stuff, ignore this segment lol
Welcome to the forum, with what you are considering, you are on the right path for sure. Generally I would say if you are after something neutral is your goal, the focal clear is a good option, although it’s not something I would call warm and thicker, but it is a great headphone. If you went with an amp like the rnhp and a dac like the bifrost 2 that would be an excellent combo for that headphone imo. If you wanted a bit more fun sound but still somewhat neutral from focal (a bit more forward, better impact, w shaped sound, more exaggerated dynamics), the elex is a good pick for sure, but it’s a bit behind resolution and capability wise from the clear.
Regarding the aeolus, honestly I would hesitate to go for it imo, as it’s kinda lacking in technicalities and imo is a fair bit too smooth for me personally, kinda just doesn’t really impress me whatsoever. It’s got a generally agreeably relaxed and warmer signature, but sacrifices the capabilities of the headphone to get to that imo. I think you might really like the auteur and eikon as that would do excellent with your sonic goals (mainly neutral, great organic impact, very detailed and refined) and would be very good with the music you listen to for the most part. You would have to look used for these to actually find them in the budget range. The auteur is a more neutral headphone where the eikon is slightly warmer and more impactful leaning. Amp and dac wise for the eikon/autuer I might suggest either something like a monolith liquid platinum or bottlehead crack + speedball for something more impactful and a bit warmer tilting with an ares ii dac, or if you wanted something more refined and neutral the hagerman tuba with a bifrost 2 is a very good combo imo.
For the lcd series, I think ideally if you could find a lcd 2.2 pre fazor or lcd 3 pre fazor those have great slam and impact, with some nice smoothness without sacrificing technicalities. Generally with these amp wise I do like the aforementioned liquid platinum for more impact and width/spaciousness with a bifrost 2, or I like the lake people g111 to really tighten them up and give them a bit more neutral character, you could look for a used soekris dac1421 later on (or a 1321)) for the dac as they par pretty well. The lcd x is very nice, personally not my favorite but I do think they are a good linear planar that is up close and personal that is more forward, I like this with the rnhp and bf2 pairing to fix the not as good timbre, but these don’t have the same smoothness and impact of the other lcd headphones
Some other headphones you might want to consider would be the hifiman arya, that would play nicely with the genre you like, and would give a pretty interesting grand and large presentation to things with good layering, my only concern would be potential treble elevation, which you could offset with something like the liquid platinum a tad, but it will still be prominent, so finding a hifiman edition x v2 might be a good play if you wanted to get into the larger driver hifiman but were concerned with treble they might have (personally I’m not bothered by the arya treble when properly amped but some still are)
I realize that what I have mentioned most likely exceeds your budget because of the amps and dacs, but I do think it’s pretty worthwhile to give these headphones a really good signal chain, if you can’t fit the amp and dacs I mentioned in the budget, if you weren’t opposed to it you could grab the amps and then grab a dac like a topping e30 or earmen donald dac for the time being and go for a higher tier dac later on (so like for a clear it would be rnhp + e30 for example and a bifrost 2 later on)
From the dacs and amps you mentioned, generally I would personally recommend against the thx amps for what you are after imo, as they have pretty overshadowed and over elevated treble, and lack good spatial recreation with mediocre timbre. The Element ii is a good dac amp combo, solid with enough power for most and clean but not boring. As is the geschelli combo. The schiit asgard 3 + modius is a warmer thicker leaning combo that’s pretty engaging and doesn’t really sacrifice technicalities so that would also be worth a look for sure.
Generally my preference would lie with the amp and dac pairings above but if you can’t make it happen even with skimping on the dac, for the elex I think the erish and enog 2 pro stack is a good pick (without upgrading your amp and dac I don’t think the clear is worthwhile), for the auteur and eikon I also really like the asgard as well, same with the lcd’s. But I do really think you are leaving a decent amount of performance on the table by not bringing your source gear up to the same level as the headphones in this range
Also since I forgot to mention gaming performance, imo mostly everything mentioned will game well for a casual or semi competitive range, although the clear and elex have some spatial presentation that can be sometimes confusing with certain games
