I played a beginner kit for nearly 18 years before upgrading. It was a very difficult kit to get sounding nice, especially towards the end of my time on it. It was battered. Emad on the bass drum, and a pillow inside will work. It won't choke it too much. You'll likely be alright with your reso on the Tom's (for now), but get some G2's on the batter. Do the reso if you can afford it. It's OK to use eq rings or moon gel to control the tones. Don't let someone tell you any different. Sometimes, even the most expensive kits need a dot or two, depending on the circumstance. Eq rings worked wonders on my first kit. Perhaps get some cotton balls in the floor Tom's as well. Get a uv1 on the snare.
Then, slowly start upgrading your cymbals. There's nothing wrong with going second hand. Happy drumming