For the original question posed in the thread. It's your call, whatever you feel comfortable with. A simple gift (like, an item or a bit of cash) cannot be considered "twinking". It's a gift. Twinking is more of an act of fully equipping a character, with gear that is far above what they could get on their own. Also, as will be detailed below, keep in mind that your first toon is the most important. This will be the one you learn the game on. But an item or two here or there, will not impact that very much.
Most people don't realize, but there are 2 "versions" of twinking. Basically as Jennock said above, but will expand a bit more.
One version is twinking your alts. Normally this is done by a high level player creating a new character for fun. In most cases, this high level character has a good understanding of the whole game in general and will use this gear to help them do their job in a group or solo. This player could play untwinked, and few would notice any real difference. It's about the ability of the player.
Version two (as mentioned above) is twinking a new player. This can create several problems. First off, you don't really learn your class (and since you're new to the game, that's all you go). You can't learn the ins and outs and what the true limits are due to the exta whatever you have. This creates a dependency on the equipment. As you get higher, and the mobs become tougher and tougher (and you eventually grow into your gear) this lack of understanding the basic game mechanics (aggro, dps, resists, special attacks, etc) will show and you will no longer be able to perform to where you should at your level. This kind of player could not play an untwinked character without covering the ground with corpses (his own, and group members').
Basically, it comes down to a basic understanding of the game being a priority. If you know how the mechanics work, any alt you create will be better than a new player at the same level (twinked or untwinked). Your skills will reach caps as it takes longer and longer to level, this is really a non-issue. Where skills really suffer, is through PLing, but that's a whole different thread :).