If you say "god" I think of monotheism. Whoever this God is, monotheism always assumes that we cannot *really* know this God. (I take abstraction from the Christian view for the sake of making a point - even in Christianism there is no immanentism - "men" can never become "god(s)"). Having said that, one can choose to deny God (atheism), doubt / "unknow" him (agnosticism, formerly deism) or start from the God idea as an axiom for further thought. In science, a impersonal origin has been postulated (e.g. the big bang) which does of course not explain origins any better - but it fits with scientific methodology because science does not start from a God idea. (Be aware that science is not necessarily contradictory to faith, as atheists often presume).
Given these concepts of God and origin, purpose can be explained without any god - for instance serving mankind, helping your neighbours etc. are purposes. With God, purpose can be lifted up to a higher plan, but it is important that you can never bypass "lower" purposes - which is demonstrated by the fact that there are some 2,000 verses in the Bible that talk about caring for the poor. Furthermore, belief in God does not make life easier necessarily - obviously there is a lot of needs (like those poor) and suffering in this world, and God does not drop by just like that to solve it. Christians may find this frustrating and non-believers sometimes tend to think of this as an argument against God, or proof of believers being foolish. Yet this frustration does not necessarily make believers passive - on the contrary it may make them more active, because obviously God's way is to work through human hands (at least for now). Maybe this helps to put things into perspective. Purpose may well be a human thing and a divine thing at the same time.
About the suffering, many answers have been given. Probably the best known among Christians is C.S.Lewis' book "The Problem Of Pain" - well worth the read. Maybe most importantly, without the God-idea the suffering of mankind does not go away: nature remains cruel, Pol Pot's come and go, and criminals of all kinds may kill innocents for money. The God-idea does not solve that nor really explain it. Yet God seems to offer solace in some of the greatest pains. Sometimes, people who suffer start to hate God, but others are attracted to God. In this realm, fixed answers will never satisfy everyone. Everyone has to make up his/her mind, but to have an open mind towards the possibility of a God above is always a good idea.
