Don't use a campus board until you are already an experienced climber, or have comparable well-practised tendon strength. The campus board is an extremely common cause of injury because of the amount of stress it places the tendons under.
Finger strength has a different idiomatic meaning to grip strength. Grip strength is how much force you can exert through your forearm muscles onto something you are clenching in your hand. Finger strength is static strength, it's what climbers engage when hanging from a hold with their hand locked into some rock-solid claw shape, and it comes largely from tendon strength, of course with some isometric muscular endurance required too.
Tendon strength can only be built up through a very long and gradual process of repeated work; while muscle can recover from training and grow in 8 days, the tendons take at least 2 months. So ease yourself into tendon/finger strength training, don't push yourself too hard at the start or you will get injured.
Frequency and volume is far more important to strengthening tendons than intensity is. Just do some low intensity tendon work every day.
You can use a hand gripper for high reps, or play with a powerball forearm trainer (I find these quite fun to use and quite physically therapeutic, it helps me avoid wrist pain when handstanding). These will also get blood into your forearm, feeding your tendons which normally receive low amounts of blood (one of the reasons they recover slowly). Also you could start doing more hanging exercises in general (for example, pull ups which you are already doing).
Do hand mobility and wrist warm up exercises every day, especially before handstanding.
And progress to finger pushups; for example, fingertip (both hands) pushups on knees, one hand variation, fingertip pushups in a standard pushup position, incline variation first, then level, then decline. Be careful to progress these very slowly and keep the intensity very low; the point is to gradually build up your tendons, you won't be able to feel your tendons working but subject them to a little training frequently and they will get stronger. If you do too much too soon, for example to the extent that you feel sore from finger training, you are on the road to injury. And tendon injuries are the worst and take forever to recover from.
When you have become used to hanging from a bar, by doing it often for a month or so, you may be ready to start finger board training (different to a campus board). You can follow any "beginner climber" finger board routine. Training on a fingerboard is the most effective way to increase finger strength, but only after you've built yourself up some strength with the other exercises so that it won't injure you.