I wouldn't even give experience when running, I'd just tell everyone when to level up. More control over the speed of the campaigns progression, more balanced player characters (against each other) and no "competition" for experience points.
That's easy for you because you have years of experience as a GM. For new players and GMs it's IMO good to have XP guidelines in the rules and use them. And the goal-based XPs of HARP or RMX can help avoiding the "competition" for XP you mentioned. Later it is possible to use shortcuts just as you do and simply tell players when to level up.
In RM we eventually got rid of individual experience and just gave group experience with a couple of the GMs who run our games. There were a couple players who were particularly bad about it, but everyone would occasionally take the opportunity to 'steal' experience when presented. Basically if one character had pounded down a foe for some time and they knew he was about to go down they'd try for the last blow to get the kill experience. This was mainly a problem with ranged combatants as they could switch targets on a whim.
However, I don't know if doing what I suggested would really be a problem for a new GM. All you'd really need to know is what you wanted the pace of progression to be in your game. Where we only play once a month at best anymore I'd pretty much have everyone level once per session (likely at the start or end of the sessions) until they really started reaching mid to high levels (maybe level 10), then I might slow it down to once every two. Of course, if you're playing a lot you'd want to slow that down most likely.
Also, I'd never start the players over level two at the most anymore. If anything I'd make them run through a minor task or mission and level up after they complete it. You could do this over the course of three to four missions for the first session and have everyone up to level 4-5 on the first go round. This gets them up to a more survivable level while limiting the unrealistic DP dumps into certain areas. This does take experienced players who are going to do their level ups fairly quickly though.