If you decide to start your investment portfolio with a lump sum of cash then the minimum amount you need will differ depending on a few factors. First you need to decide if you want a full service Financial Advisor or do you feel like you can take on this task solo dolo and will make the right decisions.
If you feel that you need the reassurance of having an advisor then you will generally look to find them looking for you to invest between $3,000 and $5,000 minimum. There are a couple however that will consider working with a minimum balance of just $1,000 but you will need to search around for them.
The internet game is a little different. There are online services where you are responsible for your own investments which will allow you to open accounts with as little as $500. Of course this will help you to get started in the market faster and the returns can be higher but you need to be extremely confident in your decisions as well as have extreme discipline.