I'm not sure we can we specifically answer the question with the information given, but below are some ideas of what to do and what not to do that may help you determine the best course of action in your own scenario.
Automate the sign-in after sign-up. I really dislike those sign-ups that gather all the site needs to use an account then redirect users to a login page to enter the information again. It's such a lazy way to link the sign-up process to the logged-in state. It doesn't take much to automate or skip the sign-in process. Redirecting to the log-in page just makes every user do the work for you instead of the dev having to connect the dots just once.
Don't ask for more right away. As a general rule, it's not a great experience for users to enter the information needed for sign-up and then after 'entering' the site to be presented with another bunch of information to fill in. Better to use a process of gradual engagement for gathering profile information including that which is often asked for during the sign-up process.
Don't lead users into a cul-de-sac After sign-up, users will be thinking "OK, I'm in - now what", so don't lead users up a dead-end which might leave them wondering what they can do and where to go. But on the other hand don't make onboarding an overwhelming experience by bombarding them with information all at once. Give one or two common options for them to explore.
Transition the experience from sign-up to usage. Sometimes, after sign-up there can be a negative feeling of having been sucked in to the site only to immediately lose control. This happens as a result of a disconnect between the high point of having logged in and a lack of a corresponding welcome to the site. I'm not suggesting an over-the-top. "HI! Great job! You did it! Congratulations!", but sometimes a feeling of "Aha, we've got your details thanks, now lets get down to the business we made you sign up for" can make the user's emotional level dip below the plateau rather than lower gently.
Provide continuity. If you know where the user came from, for example via an affiliate link or a friends referral, or if the user was already on a 'working page' then don't automatically ignore or discard this after sign-up, but provide continuity from being 'outside the site' and being 'inside the site'. Acknowledge any relevant referral, offer, discount, connection, or re-instate the previous working page as applicable. This makes the sign-up process seem less like a separate step, but part of a smarter connected service. Note that the relative usefulness of plonking the user back where they were (like after some alien abduction), and guiding the user inward or onward is entirely dependent on the circumstances of each individual site and the subsequent user expectations. You may, for example, find it best to provide several options of where to go now, one of which is 'back to whatever page'. This is also part of 'information wayfinding' below.
Give new users a lifeline. Don't ignore the fact that the user might need help. Make sure as early as possible that users know there is help available and where to find it if they need it. Just please don't make them read it right away!
Don't leave big empty voids. In sites that provide or store content, it's pretty common to present the user with some empty state to show that this is where the content will be, what the content might consist of, and to directly (or indirectly) prompt the user in trying to start filling that empty state with something. There's many ways to do this and EmptyStat.es is an interesting collection of examples.
Don't lie (or appear to lie) about functionality before sign-up. New users may have an element of mistrust or doubt about a service. Don't give that seed of doubt a chance to grow or you may find you can't ever get over it.
Information wayfinding after sign-up is critical. Often after sign-up users wonder if they are actually in the right place, for example they might wonder whether the service lives up to the claims made immediately before sign-up, or whether the service makes it easy for the user to achieve their tasks. If the functionality is difficult and the access to that functionality is hidden or not clear from the outset, you might well find the user signing out or deleting their account much sooner than you wanted, and without exploring further to find out more. So make sure your information wayfinding strategy is thought out.