Your top question is
very broad. The only answer is, just how deep in this do you want to go? I find it absorbing, and like it for a hobby. Others just want a solid vape to keep them off the killer sticks and don't want to spend any time worrying or fooling with it. Figuring out where you fit on that spectrum is part of the journey. Your second is much simpler: no, not all of the stuff is going to work together and some of it can be dangerous if you don't know what you're doing. If you take a 650mAh eGo battery-- the kind that comes in the $20 all-in-one kit, just add juice and start vaping-- put a 510 adapter on if it and then top it with a .05 Ohm cloud blowing dripper, when you push the button that battery will be glowing red hot in about 2 seconds and on fire in twice the time. You really don't want to go there. Another big question is just what kind of vape do you like; a thing you can only answer through experience and trying different styles. Some folks want a vape that makes huge clouds and blows them up like a balloon when they push the button. Others prefer it smaller and cooler and less noticeable when they exhale. There's no such thing as a "right answer" to this. It's about what you like, and why you vape. Budget is still a further question. I, for example, DIY my own juice and am not into complex flavors and chasing down the last subtle nuance of ethereal flavor like an oenophile. I make my own juice for less than 5 cents a ml, and once I get a flavor I like usually churn it out in 4oz bottles. Other folks will pay 50 bucks for a tiny, tiny bottle of gourmet juice or slave for days over the DIY kit, getting the just-exactly-right flavor they're looking for in their world famous Double Chocolate Mocha/Gooseberry/Mint/Creme Brulee/Wild Raspberry with Chicken and Waffles flavor they're working on. And none of that even considers equipment.
Assuming you're just starting out, and your real purpose is quitting smoking, here's some hints:
1) Good juice is important. Very important. I don't mean expensive; I mean it has to be a flavor you like well enough you'll be willing to take it rather than a smoke, and it has to deliver a vape, with the equipment you're using it in, that both satisfies your psychological need for the hand-to-mouth motion and deliver sufficient nicotine your body isn't either in withdrawal or overload. You need to be able to vape as often as you feel the need to reach for the machine instead of a cig, and get the right amount of nic when you do. That's how it helps you quit. There's no way to get there but try them, a thing most vape shops are set up to do. Finding a local juice brewer with flavors you like is a thing of beauty: they might let you buy in bulk to save money and, if you do, they'll tweak the formula a bit to suit you. Many online juice outfits will offer various combinations of PG/VG and different nic strengths in the same flavor, and also offer an extra flavor shot for a fee. Lots of people buy their favorite flavor with 3 times the nic strength they want and a triple flavor shot, then dilute it 2x the volume with a PG/VG base they make themselves to save money. Most of the online outfits, and many vape shops, also offer flavor sampler packs; 5 different fruit flavors, maybe, each in a tiny bottle, just so you can try.
2) Expect to try several different types of gear. Really, trying different vape styles is the only way to settle on which you like. I was chatting yesterday with a lady who likes a 9 watt vape in a 3 Ohm disposable cartomizer. And with a guy who's looking for 150 watts to blow huge clouds from a .2 watt RDA. You're not going to know which you like better until you try them both. A good vape shop will let you try them out before you buy, and many vapers will let you use their gear for a puff or two-- you just take the drip tip off whatever you're using and pop it on their gear to not spread germs-- to get a hint. Get out there and mingle
3) For a beginner who's ready to move on from the tiny eGo batteries and disposable cartos to some better gear, I recommend a medium power-- 20 to 50 watts-- regulated Variable Voltage/Variable Wattage mod (battery)-- and a popular tank with a variety of different Ohm replaceable coil heads. That way you can put different coils in the tank and, using the same juice, run the power up and down on the battery to see where you hit the sweet spot on the vape. A common choice is and eLeaf iStick in either the 30 ($30ish) or 50 ($45ish) watt model. The 30 is fairly well thought of across the board; the 50 has some quality control probs-- supposed to be corrected by now-- and some love it while others hate it. As opposed to this, I recommend Innokin's iTaste MVP mods. Innokin is a solid brand name and has been in business for a while. A bit more expensive, but no real complaints from much of anybody. Their gear works well and lasts a while. The iTaste MVP 2.0 is a 20 watt mod and can be had for less than $40 if you look around; the MVP 3.0 is a 30 watt mod in the $50-60 range depending on the sales; and the MVP 3.0 Pro is a 60 watt mod in the 64-80 dollar range online. Any of these (including the iSticks) can be bought as "starter kits," bundled with a decent tank. Depending on which mod and tank you want, these kits will run $50-$100 or so.
4) For tanks, probably the most recommended is the Kanger Sub-Tank or Mini Sub-tank. I don't have one, but these are good tanks, and Kanger is a good brand name. This tank offers 1.2 Ohm and .5 Ohm coil heads, wicked with organic cotton, a big improvement on the normal silica (fiberglass) wicks most other pre-made coils use. It also has the ability to use a rebuildable screw-in deck so you can wrap your own coils and wick them how you like, a thing no other tank in its class can do. This tank can be bought online all day south of 30 bucks; a 5-pack of the coils is $15 to $20. Other good choices for a beginner are the Aspire Nautilus, the Aspire Atlantis, and-- I like Innokin gear, I told you-- any of several Innokin tanks.
5) So look around. Ask questions here (expect contradictory opinions, too). When you settle on a good rig you'd like to try, there's a good shot you can buy the mod/tank you want as a bundle, which is the way you want to go for the best price. I don't recommend a beginner get into mechanical mods, or super high power, or rebuildable atomizers right away (an exception would be a decent rebuildable dripper clone. The vape shop will put a coil in it for you for a few bucks and, with a $3 bag of organic cotton balls from the drug store, it's real easy to wash and re-wick yourself so you can try different juice flavors easily.) You can move on into those things later-- like everything, there are advantages and disadvantages of doing so-- if you are of a mind to try.
Good luck, and sorry I got so long winded. Feel free to ask more questions. Remember, the idea is to avoid the cancer sticks.
How you do that is your business.