Have you tried resistance bands? You can use them in the same motion as some machines and have them provide resistance or assistance.

Off the top of my head I can't think of any single small weight machine that would work out both your arms and lower body.

Free weights. Get adjustable dumbbells.

For lower body, you can start with body weight and do different varieties of squats, lunges, etc. Get some free weights for upper body. A machine will limit your options and range of motion.

I love exercise machines and I am more likely to do use it. I use my elliptical and bike nearly every day for the past decade. But now I need to add weights and while I have free weights and I do use them occasionally, I just hate it and always try to avoid it. Is there a small compact weight machine I can get that will work out my thigh and arms muscles? Thanks.