How much exercise do I really need to get to lose weight? Some say 30 minutes per day, but I just read that 50 minutes may be necessary.

From my experience you can lose wieght at 30.
Some people say 3-10 minute sessions per day will work

At the moment 20-30 works for me.
If I went to the gym today and did 50 I'd burn out very quickly because I don't have the endurance nor fitness level to pull it off.
My goal is to increase my exercise to 60 minutes as my endurance and fitness level increases.

I think you're right that we need to start exercise at whatever time and level works best for us. But in the long run, I wonder if 30 or 60 minutes will be best?

I just found this info on the American Diabetes Association website:

Just How Much?
How much exercise do the experts say I need?

The Dietary Guidelines for Americans suggest how much activity Americans should do. Keep in mind they are goals, not the place to start.

People with pre-diabetes, diabetes, or the general adult public should aim for a minimum of 30 minutes most days. Walking, gardening, doing yard work, swimming, or cleaning house will all work to meet this goal. Anything that increases your heart rate and causes you to break a light sweat.
Children and teens should aim for at least 60 minutes most days.
In addition, the Diabetes Prevention Program ¿ a large study done in people with pre-diabetes ¿ showed that 150 minutes of physical activity a week (30 minutes, five times a week) helped prevent or delay type 2 diabetes. In this study, people also lost 10 to 20 pounds by making changes in their eating habits.

Do these guidelines seem hard to fit in to your busy life? It¿s not easy to find the time. You won¿t go from zero to thirty or sixty (minutes), in a day or week. Take one step at a time. Slowly build up to your goal.

Goals
Yes I think that is the key word here.

While 20-30 mins is what I'm doing now and often I can barely make that
(I did good to make 15 on Thurs.) I had to quit at that point because I was worn out.
Even though my time is low at this point I'm finding myself being able to handle more standing during daily tasks. My hip waits longer to begin hurting. I can lift heavier items w/o a problem.
But best of all I feel so much beter and I have good energy.

My goal is to build up to 60 mins of cardio 4-6 times a week.
My strength goal is to build up to strength training 3 times a week.

You definitely have lofty goals! I think the key is that you're feeling better right now, while you're building up your stamina for more exercise. We can get lots of benefits from osmaller amounts of exercise. The key is to get started - and then keep going.