If the price used to be 2.50 but by the time you get in an order it's 2.80, you're going to have to pay 2.80. You can't say, "I want to buy it at the price from an hour ago". If you could, everybody would wait for the price to go up, then buy at the old price and have an instant guaranteed profit. Well, except that when you tried to sell, I suppose the buyer could say, "I want to pay the lower price from last July". So no, you always buy or sell at the current price.
If you submit an order after the markets close, your broker should buy the stock for you as soon as possible the next morning. There's no strict queue. There are thousands of brokers out there, they don't take turns. So if your broker has 1000 orders and you are number 1000 on his list, while some other broker has 2 orders and number 1 is someone else wanting to buy the same stock, then even if you got your order in first, the other guy will probably get the first buy.
LIFO and FIFO refer to any sort of list or queue, but don't really make sense here. When the market opens a broker has a list of orders he received overnight, which he might think of as a queue. He presumably works his way down the list. But whether he follows a strict and simple first-in-first-out, or does biggest orders first, or does buys for stocks he expects to go up today and sells for stocks he expects to go down today first, or what, I don't know. Does anybody on this forum know, are there rules that say brokers have to go through the overnight orders FIFO, or what is the common practice?