To a certain extent it depends on which if the MC firms you are joining. Some have a culture where they will race you out onto your first project asap irrespective of its suitability, just to avoid the overhead of having you on the bench. Others (the higher quality higher margin firms) will be prepared to cut you some slack and ensure that you are set up to succeed on your first project by initiating you into the firm and its processes and by matching you to an appropriate role for your skills. Whichever culture it is, good advice is to be as proactive as possible in managing your own allocation to projecst that best suit your skills and experience. Thsi measn being very clear on what those are, and networkign from day one with the peopel who have a say in allocation - that's the allocation team (sort of HR-ish) and th eproject and engagement managers.
Before you join you shoud take half an hour and construct a skills pyramid. Put your number one skill/role mix at the top; if you have 7-10 years experience you might merit havign two in this layer. In the layer underneath put 2-3 strong supporting skills/roles. In the bottom layer put 5-6 things that you would be happy to "turn your hand to" based on some passign experience
When you introduce yourself to anyone that has input into your project allocation you should stress your relative expertise and role preference. The ideal situation is that they allocate you to a project that is alligned to your top skill/role. This sets you up from day one to be a big success and will accelerate your promotions prospects. You can happily accept a long term role if it fits that top layer.
That said, you don't want to be too long on the bench, so be prepared to accept a role that is alligned to one of the 2-3 second layer skill/role mixes. You should view these opportunities as positive as they get you off the bench (not good at ANY firm to be stuck there too long), and a great way to show how hard you can work and what a team player you can be. Not quite so easy to excel or push promotion, so ideally you be either trying to develop this role UP into your top layer (i.e. become an expert on the job) or get reassigned after a 2-6 mponths into your primary skills area.
Ideally you want to avoid being alllcoated to the try your hand/dogsbody stuff other than when there is serious concern that you're are stuck on the bench. Its all very well for getting billable, but you will probably end up as team dogsbody, billing at a lowish rate, undervalued, etc. The ONLY benefit is that it shows you have a good attitude, but you need to restrict these assignments to under 12 weeks if at all possible.