Ok, so first off, the guy at the gun shop is an idiot. Follow the guidelines that are outlined in a good reloading manuel and your hand loads are every bit as safe as factory loads.
I started reloading a little over a year ago and purchased the Lee 50th Anniversary kit. It is GREAT. It was low cost and came with most of the things that you need to get set-up to start reloading. The press is an "O" design meaning that it will handle the largest magnum calibers with ease and you never need to worry about the press itself flexing.
Other than the Lee kit, you will need:
Dies for the caliber you want to reload
A set of calipers
Lee Pilot & Shell Holder For Lee Case Trimmer (The cutter and lock stud come with the kit, this is everything you will need to trim the cases to the right length)
A tumbler and media to clean your brass
A loading tray to hold your brass while loading them
A good loading book (I purchased "Modern Reloading - Second Edition - Richard Lee" this seems to have a tonne of great info in it and has been all that I have needed.)
A powder trickler is optional, not necessary, but it does make things easier if you are looking to get loads exact.
As far as components go, you'll have to play around with them to see what your gun likes best. Here's what I have found personally:
Brass:
I used the brass that I had left from Federal bulk ammo and reloaded this for my .223, Federal brass isn't supposed to be great, but it sure works for me. My rifle shoots sub MOA consistantly with my hand loads.
I also use Remington brass for my 22-250. I haven't gotten it out to the range yet, but the brass seems pretty good, it is fairly consistant in weight.
Primers:
I'm sure some will disagree, but I have found that primers are primers... I use Federal and Remington and see no difference at all...
Bullets:
This is going to be different per gun. Hornady and Lapua are the ones that I use and have had excellent results with both.
Powder:
This is also going to vary a little based on your gun and what you are looking to do with it. Something to keep in mind is that the closer to full that you get the cartridge the better accuracy you will achieve. The reason for this is that when the cartridge is laying on it's side the powder is going to be very close to evenly distributed from front to back. When the primer fires it sends it's blast out in 3 directions, if the case is only 1/2 full then the blast (or blasts) that shoot upward are going to go through air in the case rather than powder and because of this they will get to the front of the case faster and ignite the powder at the front before the powder in the middle is ignited. This will cause the powder to meet in the middle of the case and the two explosions to collide with one another. You don't want this to happen.
When you pick a powder, do your homework first. The loading manuel will tell you the max loads for each powder by caliber, MAKE SURE YOU FOLLOW THIS GUIDELINE. They will also tell you what percentage of the case will be filled with the max load.
Something else to keep in mind is that you won't gain any additional accuracy (unless you are getting into long range) by going with a higher muzzle velocity, accuracy is achieved by the repeatability of your loads, having all elements as close as possible from one cartridge to the next. What WILL change with different muzzle velocities is your point of impact.