Welcome aboard Mark & friend.
There's a huge amount of information on here Mark. Discussions about antenna types and their performance. Likewise radios, batteries, keys and paddles, poles, wire etc. Use the magnifying glass icon in the top right of the screen to access the search functions. You'll be able to lose yourself for hundreds of hours reading what's been said in the past.
For your KX3, as already said, a LiFePo battery and Turnigy charger from Hobbyking is the simplest solution. There are many other battery and charger brands and vendors, but Hobbyking is a good place to start.
The 897 is not a radio I'd want to take up a hill unless you are going to carry it for me! Nothing wrong with it, essentially an FT817 with extras and a 100W PA. But it weighs just under 4kgs which is 4x what an 817 weighs and 817's are not light compared to many other radios. If it's all that that is available then it will have to do. But really it belongs back at the campsite. If you want to run it at more than 10W for any length of time, you'll need some large batteries and it (along with the 857) likes a good 12.5+ V to operate. The 817 will run down on 10V happily.
For antennas there is no right answer. Every antenna has advantages and disadvantages. Resonant antennas need no tuner and so save weight at the expense of limiting you to the bands the antenna works on. A tuner gives you more bands for more weight. If there's one built in your KX3 already then there is no issue, you'll be taking one with you.
For QRP and low power use, you can use very light guage wire. My antennas use wire I bought at a hamfest a while back, I got several hundred metres for a few pounds. It's 1.2mm PVC multistrand (0.05in) in grey. Yellow is a much better colour, it stands out against rocks, soils, green vegation and brown vegetation. I have grey because that's what was on sale. I use RG-174 coax for feeder.
To start with, if you have limited construction experience, I would make some link dipoles. They are the easiest to build with limited test equipment. There's a design on here by GW4BVE that you can build using the dimensions given and it will work, no trimming needed. I'm assuming you are both SSB only operators at present and we are approaching the sun-spot minimum, so the high bands 15/12/10m are open not too often. A 40/20/17m link dipole would be an easy starting point. When (if) the sun wakes up you can extend it to offer 15/12 & 10m.
Once you have used that and got back into radio and operating etc. you can look at making vertical and end-feds. You can make and expeirment with wire antennas for almost no cost and it's fun (IMHO) finding designs that work well as antennas but can be deployed easily on a mountain when you have strong wind and it's cold. There are more antenna ideas to play with than you can imagine. You'll find one that best fits your needs and the kind of summits you operate from.
Finally, the bit nobody has told you yet. Not only will you get to enjoy going out camping in the countryside, not only will you get to enjoy climbing up the mountains, but when you start operating from the summit, you are the DX and people chase you for the contacts rather than you have to try to break the pile up on some other station.
The other bit nobody has told you, this aspect of amateur radio becomes very addictive very quickly.