To summarize from a study published in the nlm.nih, lifting at a moderate tempo will allow you to lift more than you can at a slower tempo. This is very intuitive, as the slower you lift the more strength you exert and the sooner you will reach exhaustion. The study also concluded that there is no discernible difference in hormonal response for slow/fast tempos; however, this is not to say that your metabolic response will also be the same when lifting slow/fast. The information I've seen has been largely divided this point, with most stating that the difference between slow and moderate is negligible.
As far as recommended speed, that depends on you. It's important to realize that each technique has its own pros and cons, and you will have to weigh those pros and cons against your fitness goals and current situation to evaluate what will work best for you.
- Easy to get stuck mid-rep because you don't have tempo helping you
- Improves control and stabilization.
- Slow = lower weight, potentially lower strength gains. Most likely equivalent with moderate.
- Great for home gyms that don't have much, because it allows you to do more with less weight.
- Easy to get stuck mid rep since you are lifting heavier weights.
- Higher weights = higher strength gains.
- Moderate pace allows for you to concentrate on proper form, not speed.
- Requires access to an extensive weight set.
- Highest risk of using improper form if using high weight.
- Lowest strength gains because you don't spend enough time in the concentric/eccentric movements.
- Typically associated with low-weight and high-rep, which gives low strength gains but high endurance and conditioning.
Naturally, some of these rules will not apply in all scenarios (doing 5 second pushups doesn't require an extensive weight set, just a fit body), and some of these rules you won't care about at all (maybe you're a member of a gym). You'll have to come to these conclusions on your own.
Bonus: there is actually more to tempo than just going slow/medium/fast; for example, you might go slow on the concentric part of the lift, and moderate on the eccentric part. Here is a good article on the types of variations of tempo can you do, and what their benefits are.