Like many beginners, I bought myself a set of dumbbells to start with. You will not need very heavy dumbbells at first, but it is very important that you have the opportunity to use more weight when you reach a higher level of fitness. Therefore it is highly recommended to buy adjustable dumbbells. Which means you can add or remove weight plates to adjust the weight to the specific exercises you are going to do. You have dumbbells with 30mm and 50mm disks. That is, with holes of 30-50 mm. Make sure you pick a bar with the same thickness as the plates, otherwise they do not fit. If you are very serious about your home-gym, you might want to buy 50 mm disks and bar(s), because those can take more weight.
You can not do a lot without it. If you will only be doing bodyweight training then you will fail miserably if you do not have a pull up bar. There are various bars you can buy, including a doorway pull up bar, wall mounted bar and a freestanding bar. The choice is up to you and relies on your finances, space and personal preferences. One thing you do have to make sure is that the bar is heavy enough to hold your bodyweight plus some additional weight, just in case. It would also be nice if you had the possibility to perform different variations of pull ups like close grip and wide grip pull ups, so keep that in mind when you look at the length of the bar!
Even though I personally am not a big fan of cardiovascular exercises, I would make a fool out of myself to no recommend you to do any form of cardio every now and then. It will help you to burn some extra calories and that will indirectly lead to weight loss (for more, see the section "Weight loss").
When purchasing a jumping rope it is important that the rope is not to long and not too short. The cheapest ones often are good enough, but make sure the rope is heavy enough, so it can twist with a good speed. Aero/Speed jumping ropes are cheap and very for cardiovascular activities. Do note that jumping ropes usually do not last extremely long. Depending on what kind of floor you are skipping on, it will probably break sooner or later.
Running shoes are quite expensive, but if you like running you should buy a decent pair. The best option you have is to go to a running store where they can help you to find the right pair. Make sure it is a shoe of decent quality and that it fits perfectly. Try on your shoes in the afternoon as your feet are more "swollen" around that time. Shoes that fit in the morning might hurt you in the afternoon or evening!
(When you have a low budget and/or are not seriously considering getting your own)
Home-gym, then this is pure luxury. A bench is good equipment when you are working with a barbell and if you are working with heavy dumbbells. Ideal for performing exercises like bench presses, skull crushers and triceps kickbacks.
Lifting very heavy weights without having the possibility of using a bench is not safe. There are different kinds of benches and it is probably the best to have one with plenty of options, but without unnecessary additions. An adjustable bench is very useful when you want to do inclined and declined bench presses. Another great addition for those seeking for a bench for bench pressing is the bench with added vertical bars on which you can place the barbell after pressing. A separate squat rack can be used for this as well though!
Only buy what you need, the addition of a leg developer is nice, but if you are never going to use it, it is a waste of money and space.
This is one of the equipments you will need to have if you are performing bodyweight-only workouts, but is also very useful for those who want to do various exercises. Useful for doing dips and knee raises. Try to find one that has adjustable side bars, so that you can do different grip dips. You may be able to find a dipping station combined with a squat rack. There are also power racks that can contain dipping bars.
Barbells are not really luxury, but if you are not willing to buy more than just a set of dumbbells, then it is not really necessary. Barbells can usually take more weight on it, so you can perform heavier exercises. Certain exercises, like squats, bench presses and deadlifts are easier to perform with a barbell.
You have bars with 30mm and 50mm disks. That is, with holes of 30-50 mm. Make sure you pick a bar with the same thickness as the plates, otherwise they do not fit. If you are very serious about your home-gym, you might want to buy 50 mm disks and bar(s), because those can take more weight. This kind of speaks for itself, but I though I would point it out.
When you have a set of dumbbells to work with and / or only do bodyweight exercises, a squat or power rack is completely unnecessary. On the other hand, if you have a barbell and perform heavy exercises with it, you must have a squat or power rack to safely work out!
Find an adjustable squat rack if possible. Especially the vertical bars need to be adjustable (which, in most cases, is).
A power rack is usually very expensive, so make a wise choice and see if you really need it. A squat rack is cheaper and often easier to use when you have limited space to work out!
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