The only advantages of alkaline is the price and common availability. Other than that, they suck. They leak and corrode, and they can't handle the higher drain of powerful devices very well over time. If it's cold (Iowa gets cold), performance suffers. Avoid alkalines unless there's no other choice (like a natural disaster).
Lithiums work great, and no, you shouldn't have any problems using them. They do start off a bit "hot", being 1.6 or 1.7V, but that shouldn't damage anything. They give a steady stream of power, last a long time doing it, and last a very long time in storage. Lithiums are great to have on-hand for emergencies/outages at home, or in a glove compartment flashlight because you'll know they'll work when you need it, and they won't leak. It's never a bad idea to have some lithiums on-hand "just in case". It's also not a bad idea to have some sort of USB charger that runs off of lithiums, so you can charge your cell phone in an emergency (for example, the recent hurricane - I forget its name - that clobbered the East Coast). The only real disadvantage is cost. Just don't buy Sudaphed at the same time.
Ni-MH rechargeables is the way to go for daily usage. Despite the lower voltage, they outperform alkalines. The disadvantage is initial cost (batteries + charger), but the obvious advantage is that they're rechargeable, and if you use them frequently, you'll save money over time. The not-as-obvious advantage is that you'll find yourself using your flashlight (or other devices) more because you won't be worried about how much juice is left. Use it, then pop it back in the charger when you want to top them off.
Now, it's important to note that there are 2 types of Ni-MH. Regular ones, which have higher capacity, but quicker self-discharge rates, and Eneloops (or equivalent), which have slightly lower capacities, but hold their charge in storage better than the others. If you use your device every day and recharge frequently, the regular high capacity ones might be better. If you only occasionally use them, and less occasionally recharge them, the Eneloop types are probably the better choice. You can buy Eneloops by searching for them online, or you can buy them in stores, in which case they'll be distinguishable by being advertised as "Fully Charged", and or "keeps its charge". It's up to you and how you expect to use them that you should choose which to get. Personally, I have a mix of both that I use for different lights or other gadgets.
