The fastest and best way to improve is to take lessons. Here are three very good tennis-teaching organizations in the USA:
Each of the three web site above has a function where you plug in your city and state, or zip code, so that you can see if there are teaching professionals who are credentialed and teach at facility near you. Being certified or not certified does not a guarantee that the coach will work out for you, but it takes a certain amount of study & work to become a certified teaching pro. Coaches are not all the same.
Private instruction is usually your best value, but group lessons are also very good and have a "magic all their own," as Vic Braden once wrote. If you can do both without injuring yourself, do it :-)
This is a *skill* sport, somewhat like piano, chess, karate, etc. Measure your improvement in YEARS, not months or weeks. It takes several years to become a strong player.
***I'm on a budget, so I can afford about $300 to invest towards this.***
You could easily spend the entire $300 on one racket with a nice string job, and maybe 10 or 20 cans of tennis balls.
If you can only spend $300 for the rest of 2011, then look around at big box stores like Walmart, Target, Costco, Sam's Club, etc and get a cheap racket. You will need to get the grip size right. If you mess that up, then you might injure yourself at some point down the road. Look for a nice light frame you can easily swing on both your forehand and backhand sides.
To cut your costs further, look for pressureless tennis balls. Regular balls go dead a short time after you open the can. Pressureless balls never really go "dead."
So now, let's say you've bought a $50 racket and spent another $50 on a starting supply of two or three dozen pressureless tennis balls. That leaves you with $200.
Let's assume you already have some shorts, shirts and tennis shoes you can wear that are acceptable. If you need tennis clothes and shoes, that can easily deplete remaining $200. Good tennis shoes are a must, you don't want to injure your feet!!! Unfortunately, tennis-only shoes are often at least $100 a pair.
You need to find a teaching pro to help you learn how to hit the ball. Once you've done your research and found a good teacher, you give him or her the remaining $200.
If you take private lessons, that will give you as many as 3 or 4 lessons, or as few as one or two lessons, depending on the skill and/or notoriety of the teaching pro. Group lessons will give you more lessons, but the teacher cannot focus on you, so you don't get the same "bang for the buck."
If you don't have a local tennis shop to help you, here are some online retailers that have a lot of information:
Sportsmanship might not be #1, but it's way ahead of whatever is in 2nd place :-)
Best of luck; hope you have a little fun with it as you struggle to become the best player you can be :-)
Some books to help you get started:
Coyle, Daniel. "The Talent Code." Bantam Books, 2009. ISBN: 978-0-553-80684-7. Subtitle: "Greatness Isn't Born. It's Grown. Here's How."
McEnroe, Patrick, with Peter Bodo. "Tennis for Dummies," Wiley Publishing, Inc, 1998. ISBN: 978-0-7645-5087-4.
Milligan, Kris. "The Family Guide to Tennis." Published by Kris L. Milligan Tennis Services, 2010. ISBN: 978-0-615-35820-8.
Pluim, Babette, M.D., PhD., and Safran, Marc, M.D. "From Breakpoint to Advantage," Racquet Tech Publishing, 2004. ISBN: 0-9722759-1-6. Subtitle: "A Practical Guide to Optimal Tennis Health and Performance."
Wegner, Oscar, with Ferry, Steven. "Play better tennis in two hours." McGraw-Hill, 2005. ISBN-13: 978-0-07-143717-2, ISBN-10: 0-07-143717-7. Subtitle: "Simplify the game and play like the pros."