just tossing out some thoughts... first...if you are using historical data and attempting to using a timeframe as small as 1 minute. would there be enough representative data in each specified time frame? second...if you are considering stocks for example. should you not also consider the volume as it has an impact upon pricing per trade? third...would it not be more accurate if you use the open + close / 2 or some other similar calculation since the vast majority of trades are within this area? fourth...if you were to use high and low. would your price data be flawed because of someone that misplaces a decimal point or something like that which could cause a huge price spike?
1 minute might as well be an eternity IMHO. For any active product, especially stocks, there should be plenty of data within any minute interval during the trading day. Obviously there are an infinite number of formulas that could be used for determining the "price"... I could define the price of a stock as the midpoint of the bid and ask times a normalized value of the outside wind speed. Isn't the answer to this "basic question" the basis of a lot of automated trading? I would chalk this up as a non-issue. Either data is good or your systems should recognize anomalies (certain order-of-magnitude anomalies like misplaced decimal points).
I would use the ask if I am buying and the bid if I am selling/shorting. If you don't do this in your models and you have a high velocity model the spreads may compromise your risk and profit calculations. Also remember that you can't buy at the end of day last trade price if it opens down the next day! So you have to buy/sell at the next ask/bid on the next trade in your model in order to be conservative.
But those are two different cases, aren't they? If you are talking about bid-ask then you are talking about values that actually don't have a real place in the trade. The price on a tick reflects the equilibrium in that specific instant, that is, what two people in the market consider a fair price. If you look at a wider time range, then you look at all the "equilibrium" moments, that is, the moments when trades are settled. In that case it would make sense to consider a value indicative of the entire timeframe, like average, variance, OHLC, or something like that.