How can I purify my mind so that I can gain confidence and believe that I can study and practice efficiently? The major hindrance for that, what I believe, is that my subconscious mind is strongly saying that I am incapable.
It is just simple. The hierarchy is sila(at least five precepts for lay man),Samadhi(concentration),and insight knowledge. To achieve this in order, the very first thing is one's strong believe in Dhamma and the meditation master who can teach you in every detail. Just like inertia, if one not yet start , it is difficult to do so. But one of the encouraging fact is the will to do so if one has, it the very beginning. Throughout Sansara, all these defilement clinging to one mind but insight meditation if properly done no matter one has all the misdeeds except the great five ones. So as a very step go to a retreat you rely on where you can find a god master, and start this hierarchy relentlessly at least for 2 weeks. If you have the basic after that you can proceed at home whenever you find time. As mentioned earlier, just to start. If concentration moment accumulate from second to minute to hour , you will find the progress.
This is one of the Hindrances which is Doubt. The best way to overcome this is wise attention, i.e., see through vipallasa by means of Vipassana as mentioned in the other answer. [Nīvarana,pahana Vagga, Yoniso Manasikāra Sampadā Sutta, Vipallasa Sutta].
meditate, if you meditate correctly, you can gain relax mind that will help you to see the problem that you have right now and think of the solution, but focus on meditating not the problem when you meditate, for beginner the best object for beginner to concentrate on is breathing, the reason is because you have it, you dont have to visualisation when you meditate, keep focusing on your breath, dont control it, just let it breath by itself, when your mind start to wander around(not focus) then take a deep breath and start it all over again. but if your real problem is your mindset that think negative about yourself, i offer you to read book: 1. The Magic of Thinking Big by David J.Schwartz 2. The Power of Habit by Charles Duhigg
I forget what the Nichiren practice is called ... Gosho? Daimoku? where you memorize the Korean Sanskrit of an entire surya (either the Expedient Means one or the Life-Span of the Thus Come One one or something) and recite it (usually in unison with the rest of the Nichiren Buddhist congregation) ... https://youtu.be/650WAvcZokA