Welcome to handloading, Ken!
A great place to start handloading would be to browse through any of the bullet and loading equipment manufacturer's reloading manuals. Lyman, Sierra, Hornaday, Speer, Nosler, etc would be good ones to start with. Make this your first purchase. The few dollars that a good reference manual costs is the best money spent. Study the manual to understand the basics of handloading. Ask around with your shooting friends or join a shooting club. Surely there are experienced handloaders in your neighborhood or community. A guiding hand from an experienced shooter/reloader can be invaluable.
As for equipment, if you shop carefully, you can save money with the bundled "starter packages" of reloading equipment. RCBS, Lyman, Hornady, and Lee make good ones. I would study the manual carefully, and then select the starter kit that offers the most value for the rifle caliber that you want to reload. You can also find good bargains in used reloading equipment at yard sales, flea markets, and gun shops.
Many reloaders started very modestly (myself included) with very basic equipment such as the Lee Loader, or the Lyman 310 "Tong Tool". They are economical, and will make very serviceable ammo if used correctly. On the other hand, a single station press is the most sensible way to go if you have only a couple rifle and handgun calibers to load. A progessive machine (Dillon, RCBS, Lyman, Hornady, etc) would be of real use to high-volume ammo users such as competition shooters and clubs.
As for making more accurate ammunition, please remember that factory ammunition can be pretty good! Your handloads can be expected to give you benchrest group sizes of about 1/2 to 1/3 of typical factory ammo at hunting distances. An exceptionally accurate rifle/ammo combination can do even better. Competition benchrest shooters make their own ammunition exclusively. Competition rifle shooters handload for the same reasons: they can control every aspect of rifle/ammunition accuracy potential.
Soon you will be like most of us reloaders. We initially started handloading to be able to afford to shoot more, and it developed into a rewarding hobby by itself in the search for better and more accurate ammunition.
Don't hesitate to ask questions and for help if you need it! Plenty of more experienced reloaders here to help you discover that thrill of making and firing your very first handloaded ammunition!
HTH
John