It depends on the device, batteries that you don't expect to last can generally be rechargable provided the appliance can tolerate the lower voltage. 90% of the time it's a non issue because anything that can't use rechargeable will leave a good chunk of unused capacity even in primary batteries.
Things that don't draw much power, e.g. clocks, remotes etc, alkaline all the way. Don't care about brand, cheapest is best within reason. Don't bother with zinc (carbon or chloride) - they are frequently a little cheaper but nowhere near the capacity. Equally lithium are better but unlikely to be worth the premium except to save weight or in particularly long-life applications.
I have experimented with low self discharge NiMH batteries but found them underwhelming, may last six months in standby style use but not much more than that. Those were Amazon-branded AAAs, picked up a pack of precharged AAs from Lidl a couple of weeks back, not sold as low self discharge but must be to be precharged. I'll have to see how they go, 8 hi cap AAs for a fiver was worth a punt and good value even with the self discharge element.
Only place I used branded batteries is in a couple of very long-life applications, I'm thinking here of a couple of mini UPSes providing standby power to small network switches at home. For simplicity I built those with disposable batteries, they don't try to charge them. I use Duracell's there since they come with an 8 or 10 year shelf life. In the absence of a power cut you can swap them out after five years and put them into general use, giving you the standby element "for free" as it were.
