1. Congratulations! Welcome to the hobby.
The answer to which antenna is the best is "it depends". What bands do you want to use, what do you have for space, any limitations, can you mount on the house, do you have trees, do you have nothing but trees, are you rich/poor, etc. 40m and 20m are pretty much the standard bands for HF. They'll get you across the country, into Europe, etc, depending on conditions. A dipole is pretty much as simple as you can get, and it'll work just fine. It'll be good for one band (or maybe two). There are options that will get you more bands, but you'll need a tuner. Everyone has their favorites and they all have their pros and cons.
2m is where local traffic will likely be. There may not be much of it, but if you want to talk to people in your area that's what you want. Get yourself a 2m mobile, and there are any number of antennas that'll work for you. I was just testing a radio I picked up on 2m and I stuck a car magnet mount antenna to a metal waste basket lid. It's not ideal, but it works, sort of.
Coax is gonna depend, too. How far do you have to run it? What bands?
This is what I use for pretty much all of my portable operations, and the jacket is rated for direct burial so you could use this at home and be just fine. It's a good mix of easy to carry, acceptable losses, and so on. At the house I forget what I have but it's not something I'd want to carry or could carry in a backpack. As frequency goes up, most cable gets lossier. What would be good for 2m might be overkill for 40m.
If I was brand new and looking to buy radios, I'd look at the Yaesu FT-891 for HF/6m and FT-2980 for 2m. There are lots of dual band radios out there, but 70cm is not as popular as 2m. Icom and Kenwood are the other two major brands. I have almost exclusively Yaesu so I can't comment on the other brands. They're perfectly good, I just don't have any.
If you're looking for an HT (hand held), please stay away from the Baofengs. There are other options for not a lot more money.
If you're a member of a club (or would like to be) there may be people in the club with radios to sell or loan.
You'll have to give us a little more info to get better answers. And yeah, posting your call sign tells the internet who
@Atlantis is and where
@Atlantis lives.
Honestly the best advice I can give you is to get on the air however you can and figure it out from there. I fretted over coax and antennas and whatever for a long time and I ended up with nice coax (that someone gave me) and a pretty ghetto antenna that I cheaped out on, and it worked just fine. Not terribly efficient, but it worked. I've used antennas that "will never work" and talked to Europe no problem.
