How can I install budget-friendly handrails for our front steps?

Just buy metal ones that are cheap, nice looking at meet safety regulations.

New metal handrails will probably be less than building them with wood.

I agree, you can get inexpensive metal ones from your home improvement store that should be fairly easy to install.

I am wondering if you can patch or fill the rusted out bottoms and then repaint the railings? here is some ideas and hope you get your house sold soon

https://www.youtube.com/watch?v=GeL2_j5fJSA

https://homeguides.sfgate.com/fix-rusted-metal-railing-39132.html

Wood will be much more economical unless you can find a deal on metal. I would go with pressure treated wood and leave natural, just seal it. If you want to paint it, you'll have to wait 3-6 months for the wood to completely cure or the paint will peel.

Here's a good tutorial if you want make wood ones: https://www.youtube.com/watch?v=LVSggY6ULn8

You could have a welder / metal works guy replace the bottom part, and then repaint the existing one with Rustoleum metal paint.

I had that problem before and had a welder fix the rusted part and reuse the existing. You might see if that will work for you!

I would just do wood