Swimming practice for adult beginner

Kickboards and pullbuoys are certainly used as training aids by swimmers of all abilities. If you have only just started learning then a kickboard will be of more use than a pullbuoy. You might also consider using a noodle float.

One thing to bear in mind is that if you develop bad habits, these can very easily become ingrained if you practice on your own and then quite hard to break later. So it is probably better to keep it simple for now. In the pool you could do things as simple as regulating your breathing, getting used to having your face submerged. Unfortunately, for most people, there is no good substitute for a proper swimming instructor.

Which strokes are you learning ? If you are learning front crawl and/or backstroke you probably won't do much harm practicing kicks with a kickboard - but even with this you can develop bad habits quickly such as using too much knee and not enough hip; legs too far apart; not pointing the toes, which you may not be aware of. If you are learning breaststroke, there are so many things that can go wrong with the technique that I would not recommend doing much yourself for it directly. If you are going to practice kicks, try to keep the legs fairly close together, straight and let the power come from the hips, not the knees. Kicking from the knee creates a lot of drag. If you hear a lot of splashing behind you, then you are doing it wrong - the heels should just break the water, that's all. And keep your toes pointed. Finally, don't expect to be charging up and down the pool like this - most of the propulsion in front crawl comes from the arms, not the legs.

How is your overall fitness ? If it's not so good then general dryland cardio-vascular (eg cycling) and strength/conditioning exercises will be of great help. If this is the case then I would probably put this as a priority, because it may hinder your progress otherwise.

Edit, based on first comment to the answer: So you are learning only breaststroke ? Well, a noodle-float is a good aid for breaststroke. For one thing it helps to prevent you pulling your arms too far back. A pullbuoy on it's own will not be much use. The propulsion from the legs comes from a whipping kind of action that might feel quite unnatural. See if you can find some youtube videos that show you how to do the leg and arm action on dryland and try to get those right first, independently before practicing on your own in the pool.