My daughter is finishing up 10th grade, and my son is finishing 8th grade.

What are some good electives for them to take next year? We want to continue with a libertarian point of view, and it's critical that the courses are selected to prepare them for the real world.

I'm mostly looking for suggestions on personal finance, history, and social studies.  Also any good technical electives.

The ONLY answer is math. If you want them to have a GREAT life help them become GREAT at math.

I cant believe this country is going this way but I think Spanish may serve them well some day.

Other then that I have no idea.

We have the basics covered. They will be taking Algebra II and Trigonometry.   Looking primarily for electives beyond Math, English, Science, etc.

I agree, and we are discussing this as a possibility.

Don't colleges require a second language? Better to get a base knowledge in it early

Chinese

Consider balancing them out with humanities, music, art, Digital art, foreign exchange program...

Do they play musical instruments?

What are they interested in?

Have them think about what they might be interested in and study that.

I take it you are using the basic model of the school system to drive your studies at home?

JavaScript

Quality literature and philosophy.

Code. There are free code classes on line.
In addition to that and regular lessons, mine take guitar and jiu jitsu.

I'm a HS teacher in a suburban/rural upstate NY high school. Some of our electives include ceramics, photography, advanced drawing and painting, graphic arts, business math, career and financial management, keyboarding, WORD, music theory and piano, transportation technology systems, robotics, forensics, environmental science, graphic novels, creative writing, psychology, local industry (a project-based learning class; kids work with a local farm to help them reach a goal they set together that will help the farm to grow/reach the community, etc.) and we participate in the local tech school; lots of programs there.

Consider what you want them to learn about/or what they want to learn and design a curriculum yourselves... perhaps a research course targeting topics you feel are important to learn about. Decide on a driving question, scope and sequence, how they will demonstrate their knowledge, and criteria for success.

Been looking through this material. Some good stuff.

If you're free from the constraints of the school system, take advantage of that. Foundational history and philosophy—as much as possible.

Then as much practical learning as possible. Reading books from a smattering of the business guru types can fuel ideas.

Maybe at some point they could intern. Finding projects for them to run and be in charge of is great practice. Then dialoguing about those projects and how to grow them and run them better... Charity or religious organizations might provide a structure within which they could tackle their own projects. Something real. Not just theoretical.

Hillsdale college has many on-line free course videos, mainly on history and US constitution related subjects. Credit towards homeschool requirements can be applied. The following is from the perspective of being a Florida resident, and would be worth looking into for whichever state you reside in.

Check to see if the state has on-line accredited K-12 courses available. The state of Florida has FLVS.NET which is free to Florida residents, same as a public school. Courses are internet driven, including weekly interaction with an accredited teacher. For foreign language the course is usually accompanied by a weekly conversational over-the-phone quiz of the selected language. It may be open to out-of-state residents for a fee.  Look into duel enrollment at local community college, which will be free while a HS student

Home schoolers are free to participate in local high school sports teams, and this allows credit in physical education courses for home school accreditation. And this can help alleviate the 'anti social' stigma that many give to the homeschool idea. Rosetta Stone is a good place to start for a foreign language. Foreign outlets will have their news articles in both their native language and an English version. Good to practice with once the chosen language's syntax is understood. And at the same time get an understanding of another country's political and cultural perspective.

Just remember to take a good log of activities you have your children do, for validating their progress and for county/state review if your education district requires it.

As mentioned, Latin.
also
Debate/Mock Trial/Critical thinking

STEM.  If they can stomach it, AP classes can get them out of bullshit freshman/sophomore college classes.  I didn't have to take english in college due to AP in high school, as awful as that was at the time.  Would have been worse in college.

Depends on what path they want to take.
Engineering often requires four years of high school
math, up to at least analysis to get into a good school.

Four years will also help with many many hard science degrees.

That means in many places if you want to get an Engineering degree in the
future you have to decide at the end of you sophomore year in high school
to take two more years of math.

The biggest thing should be what are they interested in for a career AND
what do they have the skill to do.

Here's a thought: how much garage and/or basement room do you have and what tools do you own?  It might not be a bad idea to teach them industrial arts/shop, including welding and wood work.

Personal finance

Would it be possible to teach industrial arts/shop?  Economics and/or accounting might be good ones as well.

You really have to know what course(s) the school offers before you get specific with which subject(s) to take.