Best Weights for the job

As a trainer, I don't recommend walking with weights just because you can't go heavy enough to do much good for the muscles. You'd be better off getting something a little heavier and doing some bicep curls and triceps extensions before your walking. That way you work the arm muscles in a full range of motion instead of the static hold of a 90 degree bend of the elbow like you see so many walkers doing. Plus going a little heavier can actually cause the physiological changes in the muscle that give you definition and extra calorie burn. Even 5 minutes of weight training with a heavy enough weight will be beneficial. As for the weight to get, pick them up before you buy. Do a set of 8-12. If you can do that many and not feel like the last one is tough, then the weight is too light for you. Over time, you will need to go up in weight too, so I wouldn't recommend spending a ton on the first set of weights because you will out grow it.

If you are really untrained, you can put on muscle even in a calorie deficit. Maybe not with a huge one, but with a moderate calorie deficit it is possible, especially for completely untrained people. It is slow and you need to lift heavy weights for 6-10 repetition so that the last repetition is hard enough that you could not do another one. The reason for this is because such a person is so out of shape the body must add muscle. The reason this is not possible for people who have a fair amount of muscle already is that they are much closer to where their maximum muscle potential, while a completely untrained person has very little muscle to start with. Thus when you put demands on your muscles, you will find they respond.

I would suggest Squats, Bench Presses, Overhead Presses and barbell rows to start. They all use more than one muscle group and will provide a good foundation. Be careful with the form on all of these. If you are at a gym ask for help from one of the trainers.