for the lights start here
https://www.bikelightdatabase.com
they have reviews and beam comparisons of a lot of lights
for a taillight:
the Cygolite Hotshot and Hotshot SL are outstanding lights both are USB rechargable (friend has the SL,very nice light with a ton of output adjustment)
the Light and Motion Viz 180 Micro is a good light for night time group rides where you dont want to blind the shit out of the people behind you, also has some side lighting to it to help cars see you a little better, but it doesnt flash, it just kinda pulses... not the most attention catching thing out there for sure, it does have one of the most secure mounts to a bag ive seen clicks closed very well and has never fallen off on my bike
the Planet Bike Super Flash is also a great light... very bright and very attention catching... not as adjustable as the Cygolite, it just has a steady on or a flash mode, but the model i have takes standard AAA batteries and runs for 74 hours or more (this is my long ride light as i like that i can swap batteries on the road if needed)
my first taillight was the NiteRider TL5.0SL... to be honest when compared to other higher end lights, it kinda sucks... but it has a few blink options and it takes 2 AAA batteries and lasted for over 2 years before it finally fell off my bag for the umpteenth time and i just said fuck it and kept riding instead of stopping turning around and picking it up again and putting it all back together... but its probably the least expensive taillight out there at under $10 and it does work
there are tons of other lights out there these just happen to be the ones i have experience with
for the headlight:
i have the Serfas TSL250 from about 5 years ago... its a good light... its USB rechargeable, and Serfas makes a replacement battery that can be swapped out easily for when the onboard battery dies or if you need longer run times... it is well outclassed by newer lights
their 550 and 750 models put out WAY more light still have the replaceable battery and can also be used with an external 4 cell battery pack for ridiculous run times
my friend has the Cygolite Streak 310, it puts out more light than my Serfas (obviously) has a pretty good beam pattern...also USB rechargeable has little cutouts that let light out on the sides for added visibility, no replaceable battery though (can be bought packaged with the Hotshot SL for under $60) it is a great urban commuter or bike trail light
those are the only 2 i have experience with... neither is really top of the line.. but both work well for their current use
im going to need to get a brighter light for my roadbike before it starts getting dark early as neither of these will make me all that comfortable at 20+ mph on the bike trail at night
ive been looking a lot at the Light & Motion headlights... they have one of the best beam patterns ive seen... but the lack of a replaceable battery holds me back on those
there are some other lights from smaller or independent companies that look awesome i just dont know if i trust them to be around in a year lol
hopefully that will help get you started