We always recommend a Caesar under spinal - statistically it is safer for both mother and baby.
That said, there are occasions where it is necessary to give a GA - not enough time to get a spinal in (the true emergency Caesar), or mother unable to have spinal for medical reasons (there are a few), or regional block not sufficient once surgery has started needing conversion to GA.
Spinal issues: having it put in can be tricky and painful. Once in, you are numb from the middle of your chest down and may find it feels heavy to breathe. You can feel the pulling, tugging and rummaging of surgery but should feel no stinging, burning or pain sensation. Some women dislike the pressure sensations.
Risks: failure (rare - epidural failure is more common), headache (1:500), nerve injury (1:5000 short term, 1:10000 lasting more than 6 months); bleeding, bruising, infection (rare), high block (uncommon), low blood pressure and sickness (common unless your anaesthetist runs blood pressure meds at the same time as the spinal). Legs are numb and you can't move them for 4-8 hours.
Benefits: you're awake for your baby's birth, you don't have the risks of a GA, your baby does not get any anaesthetic, you get better pain relief (we can put morphine or diamorphine into your back with the local). Your partner is in theatre with you.
GA issues: you need meds to fall asleep, a breathing tube is inserted into your windpipe. There is a theoretical risk of stomach acids regurgitating upwards while you are falling asleep; often an assistant will press on the front of your neck to try and prevent acid spilling into your lungs (which causes serious injury to them).
Risks: damage to teeth from putting the tube in, sore throat, nausea and vomiting, allergic reaction to meds (1:2500 risk of anaphylaxis to the one used to relax muscles to get the breathing tube in). You may be in more pain afterwards without the morphine in your spinal fluid (can be given IV but ga patients seem to need much more pain tried than regional block patients). The baby may need more care at birth as they will have some anaesthetic on board and may come out sleepy - this might mean a paediatrician having to breathe for them until they wake up enough to breathe on their own, or having an injection of something to reverse the effects of painkillers. You will be sleepy for the first few hours and won't remember much. Your partner may not be allowed in to theatre as you won't need their support (you're asleep). All of the anaesthesia related serious incidents in the maternal morbidity audits relate to general anaesthesia (however there were and are very very few!)
Benefits: none of the risks of a spinal, fastest way to get you anaesthetised for quick delivery of baby in an emergency.
As far as I know there is no link between type of anaesthetic and bonding or feeding issues. You can feed a baby after a general as soon as you're awake enough to hold them safely. Some places will use an apnoea monitor on newborns if the mother is needing a lot if morphine based pain relief though.
Ultimately a spinal is better for the baby, but a GA may be better for you. I would go with your anaesthetist's advice. I've given hundreds of general anaesthetics for Caesarean section, often with the sickest mothers and babies - the elective type is much more straightforward.
I know you weren't after medical advice & have tried not to give any, but hope someone finds the above useful.