Chin ups and Pushups with your hands shoulder width apart and elbows close to your body.

_________________
“Nothing is impossible, the word itself says 'I'm possible'!” ~Audrey Hepburn

first of all, making gains will be extremely diet related

focusing on the big 3, will really help progress most of your lifts
-bench press
-deadlift
-squat

for your triceps
bench
shoulder press
dips

if you want to isolate further
skull crushers
tricep extensions

for your biceps
pullups
rows
lat pulldowns

if you want to isolate further
bicep curls
hammer curls
preacher curls

diet is absolutely paramount, make sure you have a split so you are getting good rest, and try to shoot for 10-12 reps a set, but be aiming for failure at around 8rm (in your mind mentally focus on getting to 12 reps, but be failing at 8 ), every set drop the weight about 10% and continue drop setting, 4 sets for the big 3, 3 sets for isolation exercises, dips/chinups/ab work, calf work, just shoot for failure

if you are passed an 8rm on a day, try to increase the weight 10% for your initial pump the next training session, really try to isolate the muscle groups and flex to full contraction at the end of each rep also, mentally focus on the muscle group instead of just lifting and going through the motions, for more of a chest pump to the inner focus on squeezing inwards at the end of each rep, for you biceps keep your elbows square and get your pinkies in tight towards your arms, focus on pointing them to at least parallel with your arms and really flex at the end of every rep

the wider you go on bench and pushups, the more the outside of your chest and shoulders will be engaged, this will give you more power to lift more weight, but give you less of a pump on your chest from the inside

keep a good split so your body has time to heal, if you are sore but not injured this is ideal especially when you are conditioned and know you have good form and muscle control, the micro tearing and exercise is just a catalyst for your body to become more anabolic and put your nutrition to better use, diet is primary, lifting is secondary, but you can't have one without the other to stimulate hypertrophy

I like to split

push/chest day1
pull/back day2
rest
shoulders day3
legs day4
rest

repeat cycle, keep your lifts recorded and when you reach a plateau try something new, experiment with adding/removing exercises (always keep the big 3), experiment with rep ranges and exercise interval frequency, experiment with diet/nutrition (just make sure you're getting your 1g protein per/lb, and .4g fat per/lb keep this constant, experiment with other factors) and caloric intake and rest times, then come back to the original drawing board and see if that has effected your gains at all

also if you are doing cardio while trying to make gains, stop, save the cardio and sprints for cutting season

if you find you are becoming really conditioned and can't get that burn the next day post pump, you can always add more sets

So THAT'S why you are called PUMPington....

_________________
“Nothing is impossible, the word itself says 'I'm possible'!” ~Audrey Hepburn

As someone who studied human anatomy and who's biceps/triceps are the best developed parts of the body I'll give you these:

Biceps:
Concentration Curls or Preacher Curls
Wide-Grip Barbell Curls (spread so that 1.5 more clenched fists can fit between your fist and your leg)
Hammer Curls

Triceps:
Dumbbell Triceps Extensions
Seated E-Z Bar Triceps Extensions
Reverse Push-Downs

Those exercises will isolate every possible muscle of biceps and triceps. I'd avoid bench, shoulder press, pull-ups, push-ups etc for these particular muscle groups because you need to isolate in order to progress. Although byceps are heavily included in back exercises so I'd avoid doing those 2 in the same day because you won't be able to do your back.
Also, after a couple of warm up sets, you need to do every next set until your muscles fail. What I usually do, is push myself to what I think is the last rep and then do 2 more. I usually roar like hell at that point, but they got used to it lol