Usually the essentials involve:
Food: You typically want 20+ meals worth, with 40 being better. Each dwarf eats 2 times per season or 8 times per year, and you should assume that you'll have 15 dwarves by summer's end and 25 by the first winter. The cheapest food on embark is meat, which for most domestic animals is 2 points per unit.
Drink: You usually want 40+ drinks, with 80 being better. Each dwarf drinks 4 times per season or 16 times per year. Bring several types, probably simply even numbers of all 4 dwarven boozes, to help with happy thoughts.
Tools: Axes can be done without, as you can turn a wood into a training axe after embark for very cheap, but you more-or-less must have either a pick or an anvil and materials for a pick. If you're not planning to make your tools after embarking, you can drop the anvil for extra points and just hope you can get one on the first caravan; you usually can.
Other materials: Taking a few units of cave spider silk thread and cloth in case you get injuries early can be helpful, but isn't essential. Extra wood or stone can help accelerate your development slightly, but isn't essential.
Skills: No skill is necessary on embark. Having one miner per pick lets you dig fast, but that skill develops quickly, so you can do without it. Carpentry and masonry are nice to have early (on different dwarves) so you can make higher-quality furniture faster for happiness. Having a skilled appraiser for your broker is convenient as it lets you see your fortress worth immediately and allows you to gauge the value of trades you offer more easily. Medical skills are somewhat difficult to train, so if you analyze your dwarves and find one that is liable to make a good doctor (compassionate, easily moved to pity, not prone to procrastination, and dedication to their jobs are important traits), making them one can be good, but you'll likely get medical personnel as migrants anyway.
Everyone seems to have their own preferences for what they bring on embark. Try some different mixes and see what works for you. Nothing is really essential - there have even been people who have embarked with no skills and no items and made forts flourish - but above I've outlined the basic guidelines.