Edited on 12/24/2014 to reflect release of the 3 core rule-books.
5th edition's Starter Set is decent to give you a feel for the basic rules, and outside players are not necessary. It is designed with beginners in mind, and is thus a good intro to the game. The starter set has an adventure in it that goes from level 1 to 5, while covering a lot of ground from a role-playing perspective as well as a combat perspective.
It's 20 dollars, but there's a high likelihood that most things outside of using the basic rules to create a character and joining the adventure league as a player are going to cost you more.
It does give you enough to work with to create your own campaigns as well, as the monsters in the appendix are varied enough for some play-room.
This is particularly advantageous if you don't have a lot of people in your current group and want to get going. If you just combine two groups, you might make the new group too big to manage reasonably. If there's only a couple of you it is easy and would likely be a great intro. If you have a single player you can draw in to play or DM that knows a lot about the game, it can certainly compensate on either side.
The basic rules are available on the official D&D website. They cover character creation for one of each type of fighter, cleric, rogue, and wizard as well as an assortment of backgrounds. The basic rules are free, and include monsters and magic items in the Dungeon Master documents. They won't tell your DM how to prepare a game outside of managing encounters, but it is enough to get you moving for free if your DM is willing to put in a little work.
As of the time of this update, the three core rule-books are available for purchase at online retailers and local game/hobby-stores.
The Player's Handbook (PHB) covers all of character creation, including far more options than the basic rules and documentation of the rules necessary to play that is more in depth than the basic rules (except in combat, which was covered very well in the basic rules). It is about the price of a new computer game (40-60 USD after-tax depending on where you get them). A game benefits highly from having this book, and most players end up getting one for themselves at some point.
The Monster Manual (MM) and Dungeon Master's Guide (DMG) are more for the DM. The former includes a huge assortment of monsters, beasts, and NPC templates ready for use. The latter is primarily about customizing your campaign, tuning and tweaking it for the way you want to play. The DMG also covers magic items, random dungeon generators, and a host of other resources that can be useful to someone running a game to speed up preparation and allow for customization. Typically only one of each of these books is necessary in an entire gaming group, but with the basic rules for free, the investment can wait until you are ready for it. Each of these two books costs the same as the PHB. Some groups pitch in together to split the cost for these two books, just make sure there won't be problems with book ownership after it's all done.
If you are in a hurry to try it within the next 3 or 4 weeks, then by all means pick up the Starter Set, or find someone at your local game store that has it and wants to run a game. Ultimately, the decision on how to approach this is up to you. There is no wrong path to start the game.