There are a couple of things you could do, but it may depend partly on the type of orders your broker has available to you.
Firstly, if you are putting your limit order the night before after close of market at the top of the bids, you may be risking missing out if bid & offer prices increase by the time the market opens the next day. On the other hand, if bid & offer prices fall at the open of the next day you should get your order filled at or below your limit price.
Secondly, you could be available at the market open to see if prices are going up or down and then work out the price you want to buy at then and work out the quantity you can buy at that price. I personally don't like this method because you usually get too emotional, start chasing the market if prices start rising, or start regretting buying at a price and prices fall straight afterwards.
My preferred method is this third option. If your broker provides stop orders you can use these to both get into and out of the market. How they work when trying to get into the market is that once you have done your analysis and picked a price that you would want to purchase at, you put a stop buy order in. For example, the price closed at $9.90 the previous day and there has been resistance at $10.00, so you would put a stop buy trigger if the price goes over $10, say $10.01. If your stop buy order gets triggered you can have either a buy market order or a limit order above $10.01 (say $10.02). The market order would go through immediately whilst the limit order would only go through if the price continues going to $10.02 or above.
The advantage of this is that you don't get emotional trying to buy your securities whilst sitting in front of the screen, you do your analysis and set your prices whilst the market is closed, you only buy when the security is rising (not falling). As your aim is to be in long term you shouldn't be concerned about buying a little bit higher than the previous days close. On the other hand if you try and buy when the price is falling you don't know when it will stop falling. It is better to buy when the price shows signs of rising rather than falling (always follow the trend).