Wow - LOT of stuff to go over here to help you out.
1) Transmitters are a personal thing. As mentioned before, there are a bunch of different brands. I personally like Spektrum, because in my area, all of the hobby shops carry them and carry their receivers. Also, nearly everyone at my flying field uses Spektrum, so if I have to ask a question of someone on programming, or how to set up something more complicated like mixes (don't sweat that as a beginner!) then I will likely have someone at the field who might've run into those configurations and I can pick their brains for knowledge. That could all be the same if everyone at the field is flying Futaba, or FrSky, or Jumper, or Radiomaster - you have a resource for knowledge based on the other people who are flying that same brand of radio.
I will tell you that the biggest thing for me when it comes to a transmitter is ergonomics. I played with the FrSky X-Lite a few years back at the AMA Expo, and I personally hated it. Why? Because it felt like a game controller, and some of the switches weren't easy to reach for me without taking my hands off of the sticks. That said, there are a few kids at my field who have them and absolutely LOVE the controller because it fits well in their hands. This is something that's kind of a personal fit.
Also, as weird as this sounds, (and coming back to a personal preference) I like a transmitter that has a bit of weight to it. I tried out a FlySky IX6 and it felt light in my hands. The sticks felt like they were made of plastic, and in the back of my head all I could think was, "If I panic and push hard in a direction to try and recover from something stupid I'm doing, I might end up breaking this thing in half!!!" So, another personal feel thing. You may really like that lightweight feeling of the transmitter, but for me? It doesn't work at all for me.
I see that you're looking at the Spektrum DX6e, which is a great radio which will last you for a while. There are a few minor (and I mean MINOR - I wanted the ability to hear a voice call out how many minutes I had left on a timer, for example) things that steered me away from buying one when I was learning to fly, but that's a great radio that will last you for several years until you require an 8 channel transmitter for a bigger plane.
2) With regards to the AR410 receiver:
The very first slot is the "battery" section. This used to be used (and still is used in some instances) for a battery pack to power the receiver. This way, if you ran out of power on the battery powering your motor, you would still have power for your servos to control the plane and bring it in for a landing. It's not used much anymore on the electric planes, but is still used on some of the gas/nitro aircraft, or in some of the higher end large scale planes, simply to ensure enough power to control things like landing gear, multiple servos, bomb bay doors, etc., especially if they're larger hi-torque servos.
If you are using an ESC with a built in BEC (Battery Elimination Circuit), you won't need this. Most ESCs have this nowadays, so you can just connect up your battery to the ESC and power your servos without too much fuss. Connecting up the receiver is fairly easy; the first slot on most Spektrum 4 channel receivers are either the Bind or Battery slot, followed with the TAER acronym - Throttle, Aileron, Elevator, and Rudder. Since they're not labeled as such on the AR410, it's 1-Throttle, 2-Aileron, 3-Elevator, 4-Rudder.
3) Chargers:
Chargers are varied. The more you spend on them, the nicer you'll find them to be. But this is loaded as well, because you need to pay attention to what you're buying.
A lot of chargers are DC only, meaning that you'll either need to connect them up to a 12v power source, like a car battery (it is NOT recommended to hook it directly up to your car's battery when it's in the car; if a battery gets too much charge and decides to go up, it's now taking your engine bay and car with it, and there's nothing you're going to do to stop that sucker from being a total loss), or the alternative, where you have some sort of AC to DC transformer that plugs into the wall power at home and then converts it to DC power. Some people will use computer power supplies to connect their units, buying a 400w power supply to connect and charge their batteries.
Other options are to get an AC/DC charger, which will allow you to use AC at home to charge, and DC if you're out at the field with a car battery (or like at my field, where we have a solar power charging station that's connected to a couple of deep cycle car batteries that get a constant charge from the solar panel during the day). Several chargers that come to mind are the ISDT K2 or K4, or the HiTec X2 AC Black, but others may have other recommendations.
Depending on how big of a plane you decide to progress to, you'll also want to think about charging some of the larger batteries. Most of the cheapest chargers will do 2S-3S battery chargers; some will do 4S as well. If you want to get into things like racing quads, helicopters, or larger scale or 3D aircraft, they'll likely start using 5S or 6S batteries, and the cheap chargers won't be able to charge them - or if they can, they'll charge them at a dramatically slow rate of charge, where it can take a couple of hours to bring a battery to full charge.
I currently have the HiTec X2 AC Black, which, while being a little underpowered on its wattage, has some nice features for the price, as well as an Imax B6 charger that I inherited from my father after he passed away almost 2 years ago. The HiTec charger has the ability to charge two different batteries at the same time, which is REALLY nice. I do flight instruction for my club on Monday nights during the summer, and so I'll drag my batteries and charger in to work on those Mondays and start charging them. I run through sometimes 6 batteries each training session, so the ability to charge up 2 batteries at the same time means I might only be charging for 3-4 hours, as opposed to 6-7. The HiTec's wattage does make it suffer a little on the charging time when I'm charging two batteries at the same time; it has the ability to charge with 200w, but that 200w is split between the multiple channels, so I'm really only charging 100w per channel, slowing the process down a little bit. The HiTec also has an app that you can download and use on Android or iOS, and it'll allow you to make and scan QR codes for your batteries, so you don't have to go through storage settings each time you're changing out to different batteries - simply open up the app, connect the battery, scan the code, and the charger starts charging. When it's done, it'll pop up an alert on your phone to tell you it's complete.
The Imax B6 charger works, and charges batteries, but it's severely underpowered and is limited to 50w for charging, as well as only having 1 channel to charge on. They're really inexpensive, but trying to charge larger batteries, it falls short. Charging a 3S 3200mah battery (the standard battery we use for flying in our training sessions), it can take well over an hour to charge just one.
That's where spending a little more money can get you more wattage and more features, so the trade off might be worth buying something other than the absolute cheapest option. I think that the two things to invest in at the start are your transmitter and your charger, because they'll last you for several years, and as you grow as a pilot, you'll be a little "future resistant" until you find you have a need for something more.
