Successful weight training depends on more than lifting a particular amount of weight for a specific number of reps and sets. For best results over time, you need to set up your workouts in the right way, so that your muscles are worked out in a helpful rather than harmful sequence. One broad rule of thumb is to work your muscles from large to small within each group of muscles worked. For example, in a chest/triceps/shoulders routine, you would work your chest first, then your triceps, and finally your shoulders. There are several aspects to consider when setting up a triceps workout after chest presses.
The type of routine will dictate the composition and flow of your workout, and what triceps work you’ll do after your chest exercises are complete. A full-body routine works every muscle group in each session you do. Full-body routines involve fewer exercises for each muscle group than split routines, and it means you’ll have to consider which triceps exercises will be the most effective for the limited amount of time available. You may only do two, maybe three triceps exercises, so you need to optimize. For example, following chest presses, you may do three or four sets of dips, followed by three or four sets of barbell pullovers or overhead triceps extensions.
Split routines offer more latitude for arranging your workouts, because you’ll only work your chest, triceps and shoulders during a particular session. This gives you more time to incorporate more exercises, which lets you work both the target muscles and the secondary muscles. For example, following bench presses, and after a suitable rest period of two to three minutes, you can afford to do a couple of softer routines, such as triceps presses and cable rows, that spread the stress of the lift through a couple of other muscle groups. This will warm up your triceps before you do a couple of the harder exercises, such as extensions, pullovers and dips. Split routines let you focus more on individual muscles each session, but it means more overall time at the gym each week.
For best results, whether you do split or full-body routines, group your exercises together for each target muscle rather than do a set of chest exercises, then a set of triceps exercises, then another set of chest exercises. Even though most exercises will use all three muscle groups, the target muscle is always worked harder during exercises that target it -- and you risk diminishing performance and possible injury in constant switching. Do all of your primary chest exercises, such as flyes and presses, then move on to your triceps work, such as dips, presses and extensions, then move on to shoulder work.
Also, regardless of your routine, build in enough rest time to allow your muscles to sufficiently recover in between workouts. Your muscles only get stronger on rest days, after they’ve done the work. Make sure to consume a balanced, protein-rich diet that provides enough fuel for your muscles to grow. This will give you more consistent gains over the long term. Use a spotter for exercises like the chest press and the overhead triceps extension, because the form of each leaves you vulnerable to fatigue and injury.