Depends on your budget and what you expect to get out of them. As is everything, you get what you pay for. I'm sure someone will say Shimano Calcutta reel and Talavera rods are the only ones to buy. If you have a few grand to spend on a few, I would agree. But if you're like me, I try to get the best I can afford at the time.
A typical downrigger rod will be 8'-9.5' in length with a reel that holds 1000' of line. A line counter reel is nice, but not necessary. 15-25 lb mono with a 20-30lb floro leader is common.
A typical dipsy rod tends to be shorter and more stout. Same size reel as above, but braid or wire is a better choice. The no stretch of these allows you to release a big dipsy when it is time to reel it in. A line counter is a near must have to know how much line you have out to get to the depth you want (unless you are good at counting passes).
Copper and lead core rods are typically somewhere between a downrigger rod and a dipsy rod. Reels should be a size up from the above and have a line counter. They are usually flatlined straight back or off to the side on a large planer board. As you are just starting out, you may want to consider getting a bit more experience before using these set-ups.
I have Penn, Daiwa, Okuma and Shimano rods and reels and they all work well for me. Some were bought new, some were bought used off this site. The best advice I can give is go to your favorite tackle dealer be it Bass Pro, gagnons , Canadian Tire or your local shop and find what works for you and how you intend to fish to get started.
A rod and reel combo specifically designed for one of the above methods is a good way to get started. You can always change it up as you want as you go on.
(Is that politically correct enough for everyone?