Let's start at this point:
Some exercise > no exercise
In short, if you are doing something, anything, you will make positive steps toward fitness. The problem with stopping there, is that usually the something people choose, doesn't maintain their interest. This can be a result of not perceiving any benefit, or shear boredom.
Your goals are stated in this way:
- I'm not looking to get bigger (anti-goal, a limiter of things you are willing to do)
- I just want general fitness
So the 5 million dollar question is: what is general fitness? The secondary question that is equally important, is how do I make it interesting? To answer the first question, the best way to define general fitness is to break it down into its main parts:
- Strength, the stronger you are, the better your quality of life as you can pick up heavy things, and resist injury better.
- Conditioning, the more conditioned you are, the better you can keep blood flowing through your body and you can have the energy you need to do what you want.
- Mobility, the more mobility you have, the more range of motion you have without pain. This also affects your quality of life.
- Coordination, the more control over your body that you have, the better you can get it to do what you want without thinking.
- Healthy range of body fat, too much or too little body fat will adversely affect your health. If you can keep the body fat within the range of a six pack to a flat stomach, you are in a healthy range (approximately 10-15% for men and 12-25% for women).
Whether you play basketball, run marathons, swim, or left weights, all of the above points help you achieve general fitness. The activities that go into becoming fit include exercise, stretching, skill work (drills, playing, practicing technique), and good nutrition.
The question isn't so much what you don't want to do, but what you are willing to do. You have some equipment--the adjustable dumbbells--at your disposal. You can use those to help build strength and conditioning. I'm going to assume you are a complete beginner, so anything will help. Here's an example program you can do:
Simply do these exercises 3 times per week, alternating between them each time. Make sure you have a day of rest in between.
Now, why sets of 5? Because you stated you are not looking to get big. Sets of five help work on strength in the range that a beginner should be focusing on. In reality, anything in the 4-6 rep range will work for your purposes.
Your goal should be to start out at the lowest setting on the dumbbells, and keep increasing the weight every time you do one of the exercises. With the farmer's walks, you may need to start with a lower amount of time and slowly increase until you get to 10 minutes. When you get to the max that your dumbbells can afford you, you have a choice: go and buy more dumbbells, stay at the maximum and maintain (can get boring), find a pickup sport you can play.
In addition to this, be sure to stretch after you exercise. A nice slow walk afterwards can also help you cool down and get blood through your sore muscles. This is just a simple program to get you started. The question then becomes, is this something that can keep you interested?