The first thing you should consider when you choose a laptop battery is the reputability of the batteries. There're many laptop manufacturers on the market. If your budget is not so tight, then the best choice would be a battery made by the manufacturer of your laptop. But those batteries would be much more expensive than the average price in the market. Dell, for example, has been known to charge four times more than ones you can get elsewhere. Therefore, if you don't want to pay the high premium price, you can get one from a different manufacturer.
Actually many famous laptop battery manufacturers don't actually manufacturer, instead they are the brander of the product. For instance, if you open up a genuine Sony laptop battery, you may find that the power cells inside are actually made by Toshiba, Panasonic, or a similar big name company. Many third party brands use the exact same power cells as original manufacturers, and they cost much less than the original ones.
Another thing you should consider is the type of the battery. Normally there're 4 main types of laptop batteries: nickel cadmium (NiCad) battery, nickel metal hydride (NiMH) battery, Lithium ion (Li-Ion) battery and Li-Poly battery. NiCad battery is very old and primitive; it's rare in the market now. Ni-MH is newer and more advanced, but is not as good as its Li-Ion and Li-Poly counterparts. Li-Ion and Li-Poly are the most advanced and common types of batteries on the market. You should be clear what type you laptop battery is, because most of the laptops are designed with one type of batteries and cannot be used with other types. For example, if your original hp laptop computer battery is Li-ion, then you should get a Li-ion replacement battery.
Another important thing you should really pay attention to is the power rating of the battery. Batteries with the same physical size may vary greatly in power ratings. Normally batteries are rated by Volts and Amperes, though most companies show battery ratings with Volts and Milliamperes (or mAh). One thousand Milliamperes equals 1 Ampere. However, some batteries have both different Volts and Milliamperes, then it's hard to compare which one has stronger power. Actually there's another way to rate the power: by Watt-Hours. Watt-Hours is just multiplying the Volts and the Amperes together. So you can easily find out which battery has more power.
There's one more thing you should be noted: be careful with the used or refurbished batteries. Because refurbished batteries do not hold as much power when compared to new batteries. Also, they can kick the bucket on you randomly since you really do not know how old the battery is.