Speaker/Monitor issues

The thing is there are 2 things to consider:
1. Practicing DJing. You should have decent gear for that, but even your Logitech will suffice for that.
2. Producing….
For production you need a monitor speaker.
Why?
Monitors should have 2 very distinct qualities that put them apart from HiFi or PA speakers:
a. A flat response – typically the better the monitor the flatter the response, which basically means it will in no way alter the sound and you will actually hear exactly what you put in them. This is crucial for making a good production as you have to hear your EQing, filtering, compression levels etc. etc. etc.
b. They have a good frequency range (this is also true for real good HiFi or PA speakers, but they do not have as flat response than monitors). So basically you would want to get at least 40Hz – 20kHz, real good Monitors will go far beyond that and for lowers you need a subwoofer. But again not just any sub, but one that will not color the other frequencies (aka monitor sub).

This is why often monitors in a production studio are one of the most expensive things to buy.

Now what does that mean for your current options:
Option 2 is probably the worst as the amplifier probably has no flat response either, so you get 2 times the tone coloring.

Option 3:
Usually Logitech speakers are not “that” bad, but are no monitors either. Especially their midrange is typically not flat and the sub does color sound quite a bit. If you hook that up to a good sound source (aka a good controller) you can probably get away with that for a while, but do not expect them to be phenomenal and your productions will most likely be more compressed, as the logitechs usually have not the dynamic range to hear that truly.

Option 1: Now while the headphone description says “studio”, these are low cost headphones for like 30 bucks and the membrane is not the best to begin with. While they have good bass room and some nice “oomph” they lack the higher frequency response and mid range of really good studio headphones (why good studio headphones cost more than speakers).

So non of your current options might be ideal you can still make the best of it, by trying to tune the Logitechs to your sound.
Hook your controller up to the logitechs (you probably need an adapter) and start with a flat EQ. Now get a basic synth and drum loop together and tune the sounds as much as you can with the EQ that it sounds OK, if you can alter the subwoofer level separate on your logis then go for less sub. Check that against a song that you really now how it should sound and EQ accordingly. Repeat several times and mark your EQ settings.
This will get you some sort of baseline. It is still no studio setup and you should invest in real monitors for production, but you can get away with tuning at least while you practice.

I hope this gives you an idea on monitoring and there are no dumb question, this is actually a tricky one that many do not get right even when they have monitors…

Ah I got the Panasonics from Amazon for 30 euros… do not get me wrong they are good for listening and you are right that they have the frequency range, but they have by no means a flat response and color tone quite a bit, especially in the lows and have a pretty wide spot in the mid where they are nowhere near flat. This is absolutely no problem for Djing or manual beatmatching etc. as they are also pretty loud and have good bass.
I did test them against extremely good shure in ears that are truely flat and you can easily hear the difference there…

But also consider I am really picky and sometimes things bother me, that are no problem for others. So always take my points about sound quality, response etc. also from that viewpoint…

And about THX:
The THX system is not a recording technology, and it does not specify a sound recording format: all sound formats, whether digital (Dolby Digital, SDDS) or analog (Dolby Stereo,Ultra-Stereo), can be “shown in THX.” THX is mainly a quality assurance system. THX-certified theaters provide a high-quality, predictable playback environment to ensure that any film soundtrack mixed in THX will sound as near as possible to the intentions of the mixing engineer.
So this is actually a good thing, just as added info.

Well a sound card or a controller with built in sound card is never a bad thing and you can split your signal for the headphones more easily.
If you are really on a tight budget maybe go for a lowend controller like a mixtrack pro or even the new hercules Phil just tested, is quite OK for starters and hooked up to your Logitechs should be a start before you can safe up for better stuff.