L-Carnitine is an amino acid that can be made by the body and is found in red meat. The body uses carnitine throughout the body, in tissues like the heart and brain, and has many benefits, but it is mostly know for its role in helping metabolize fat, shuttling fatty acids into the mitochondria to be used as fuel.
To help with fat burning you could take some carnitine tartrate and it would do sufficient job. I like to use higher doses in the 6g-10g range, spread out throughout the day. I take this before 2pm as it can be stimulating for some people and no more than 2g at a time.
For brain benefits, then acetyl-carnitine is a better choice as it crosses the blood-brain barrier. It still has the other benefits of carnitine so you won't miss out on any of the fatty acid utilization you might get with regular carnitine.
Taking 1-4g of acetyl-l-carnitine per day is a typically type of dosage but I tend to take a little more. Use what you feel is working best for you and what fits in your budget.
Acetyl-L-Carnitine can help with memory, alertness, and has neuroprotective benefits. It does this mostly by boosting acetylcholine levels in the brain. It can also increase brain derived neurotrophic factor and promote circulation in the brain.
For these reasons, I began taking acetyl-l-carnitine about 10 years ago as part of my "stack" to help restore / improve my brain function after suffering many concussions. It has worked well and I keep it as part of my daily supplements as it has many benefits. Using it pre-workout is also very good to help with focus throughout your workout.
Another thing is r-form alpha lipoic acid and fish oil work synergistically with carnitine so I combine these as well for greater results. Also I take these along with alpha gpc, a racetam, and CoQ10. This seems to be working quite well.