Here's the list of all primary perks which will become available each time you advanced to a higher level of experience. Notice some of the perks have strict requirements, not only when it comes to achieving certain level, but also having developed skills. It's up to you whether you want to focus on fulfilling these requirements or not. Some of the perks are available more than once and obviously each time you choose them again the effects of having them will be stronger.
Chart description: lvl - required level of experience; ranks - how many times you can choose this perk; req - additional requirements
INTENSE TRAINING - lvl2; ranks: 10 (!!)
Effects: Each time you receive one point to be spent on a primary statistic (S.P.E.C.I.A.L.) of your choice
Additional info: I think this is a very interesting perk, especially if you want to have a character who specializes in all sorts of activities and doesn't have any weak spots. Don't forget not to spend points on stats which can be acquired using other means (for example - after collecting a bobblehead or after fulfilling a quest).
LADY KILLER / BLACK WIDOW - lvl2; ranks: 1
Effects: 10% extra damage dealt to characters of different gender, new dialog options
Additional info: Black widow is by far more interesting than Lady killer, because there are more men occupying the wasteland and the 10% bonus is a lot, especially when dealing with stronger foes. New dialog options might seem like a good idea, but won't be many of them and usually you'll achieve more by winning a speech challenge.
LITTLE LEAGUER - lvl2; req: Strength 4; ranks: 3
Effects: Each level raises your Melee weapons and Explosives skills by 5 points.
Additional info: A relatively weak perk, especially since you should spend 3 points to notice effects of your actions (15% bonus).
SWIFT LEARNER - lvl2; req: Intelligence 4; ranks: 3
Effects: Each level raises the amount of gathered experience points by 10%.
Additional info: Similar situation to Here and now perk. You should only be interested in this perk if you want to advance as fast as possible. I assure that you won't need it and that you'll get to the 20th level of experience without its help. Spend your perk point on something else.
DADDY'S BOY / DADDY'S GIRL - lvl2; req: Intelligence 4; ranks: 3
Effects: Each level raises your Medicine and Science skills by 5 points
Additional info: Similar skill to Little leaguer, but obviously you can count on other skills being raised. I would recommend ignoring this perk, because you can get a similar amount of skill points by finding books or bobbleheads.
GUN NUT - lvl2; req: Intelligence 4, Agility 4; ranks: 3
Effects: Each level raises your Small guns and Repair skill by 5 points
Additional info: In this case you should really consider investing at least one point, because both skills are very useful. You'll be using small guns very often and the possibility of repairing them is also important.
THIEF - lvl2; req: Agility 4, Luck 4; ranks: 3
Effects: Each level raises your Sneaking and Lockpicking skills by 5 points
Additional info: Obviously you should consider choosing this perk only if you're planning on playing as a thief. Otherwise you can ignore it.
CHILD AT HEART- lvl4; req: Charisma 4; ranks: 1
Effects: new dialog options when talking to children
Additional info: This isn't a useful skill, because the only thing it does is that it opens new dialog options. Take it only if you want to play as a negotiator. In such case you should choose it along with Lady killer / Black widow perk. Otherwise you should spend a point of something else. You should also know that there aren't many kids in Capitol wasteland. The only area worth mentioning is Little lamplight.
ENTOMOLOGIST - lvl4; req: Intelligence 4, Science 40; ranks: 1
Effects: 50% additional damage to insects
Additional life: You may be surprised to hear that it's an interesting perk. Eliminating radroaches is a piece of cake, however you can have more problems getting rid of radscorpions and fire ants. This is when this perk comes into play.
EDUCATED - lvl4; req: Intelligence 4; ranks: 1
Effects: Three additional skill points to redistribute each time you've advanced to a higher level of experience
Additional info: Unlike Swift learner this is an extremely useful perk and you should take it when you advance to the 4th level of experience, so you won't lose any bonuses. Having additional skill points is always a good thing.
COMPREHENSION - lvl4; req: Intelligence 4; ranks: 1
Effects: Two skill point instead of one after reading a book
Additional info: This is an interesting proposition, but only if you like to explore your surroundings in search of books and other valuable items. This will make your progress a lot smoother. If you don't plan on collecting many books you may ignore this perk.