Players have different preferences when it comes to rackets. Rackets are made in three different shapes, round, teardrop and diamond. Each of these different shapes can be made using different materials, but most of the time, the racket itself is made from Fibreglass or Caron Fibre and the centre of the head is made with a foam or rubber. For the vast majority of players, they will not notice a major difference in the balance, they might notice a minor difference in the weight, but you will almost certainly will feel a difference between a hard and a soft racket. The softer rackets provide more control and harder rackets more power, although most rackets will combine both elements.
The ball looks like a tennis ball, but it is slightly smaller and has about 20% less pressure in it, making it less bouncy. There are a many different brands on the market, some more pressurised than others, making the game faster, so depending on your level, those are the balls that you should be using. The less pressurised for beginners and the more pressurised, faster balls for the more advanced. For the recreational player, you do not necessarily need new balls every time you play, a can of balls should last you a few matches, before they start going flat.
When you first start playing, you will get away with a tennis shoe, but for better grip it is worth looking for a pair of specialist Padel shoes. Clay court tennis shoes will often do a good job for the majority of players. The only difference between the clay court tennis and the padel is that the grooves (shaped in zigzags) are often slightly deeper in padel shoes.