1. Build Your Gas Tank
If you want to get the most out of wrestling practice then you need to get fit, if you gas out quickly so will your ability to learn. If you can build your fitness to a reasonable level so that it's not so much of a problem when you start, then you'll be in a much better position to learn and most importantly reduce your risk of injury. Think HIIT using whole body cardio equipment like rowers and echo bikes (my personal favourite). Once achieved, you can then really hone in on your specific conditioning which is essentially just wrestling.
2. Build Neck Strength
Head control is a significant technical component of wrestling. The head can be used to control your opponent, set up techniques, push and drive and help resist getting pinned on the mat. If you have a weak neck then you're going to find it difficult to recover from lots of wrestling and it may get to a point where you'll need to take time off to rehabilitate. Consider strengthening your neck first using various isometric and dynamic exercises including controlled forward and backward neck bridging, think of these as "regressions" like doing assisted pullups before bodyweight pullups.
The reason why I'm only mentioning the neck here is because i don't think a lot of people train their necks, even if they have a few years of strength training behind them.
If you're new to strength training, you will most likely need to focus on building all round upper and lower body strength as well as neck strength. To learn how to do this while wrestling, check out my last article here.
3. Build Some Agility and Co-ordination
You'll pick up a lot of this from just wrestling but it wont hurt to get your wrestling co-ordination up with some low intensity change of direction drills such as lateral and rotational hops and jumps. You could also try doing some shadow sparing, Cary Kolat has a good shadow sparing tutorial on YouTube or head to this website for tons of educational content.
Check out all the factors that make up excellent agility which can take years to develop.
4. Get Springy
Given that wrestling is a high intent, high speed sport you're going to want to focus on improving your ability to utilise what's called the stretch reflex.
When a muscle is rapidly stretched, specialised muscles send signals to your spinal cord to rapidly contract that muscle, producing a lot of power (check out image 1). But you have to be quick to catch the stretch reflex because it only lasts a few milliseconds (why i mentioned that wrestling is a high intent sport). You also get some power from the connective tissue lined between layers of muscle and tendons, they act like elastic bands that snap back when stretched (check out image 2).
Yes you'll develop your stretch reflex by just wrestling and you do have to get your wrestling technique down pat before you're able to fully utilize the stretch reflex simply because you dont want to waste time thinking about how to do a move, you just want to GO!
Build general springiness with simple hops and jumps. You can even just start your workouts with 5-10 minutes of skipping or again, shadow wrestling.
Image 1
Image 2
5. Respect the Process
Wrestling is a sport of skill, intelligence, intention, commitment, reaction, manipulation, strength, power and endurance, don't get distracted by needing to be tough because it's going to take a lot more than that to become a half decent wrestler. Don't be afraid to back off live wrestling if you think you need more time to adapt to the wrestling environment, practice stance, motion and technique (best injury prevention tool btw). Yeah some flog might call you a bitch, who cares, leave the ego at home. Take your time, think about wanting to be at a reasonable level in 5-10 years not 6 or 12 months (if you really want to get somewhere), especially if you're a late starter.
Suggested Readings
Thomas. RE, Zamanpour. K. Injuries in Wrestling: Systematic Review. Phys Sportsmed. 2018 May;46(2):168-196. doi: 10.1080/00913847.2018.1445406.