Honestly, no. I have had an orgasm through the cage with stimulation from a vibrator, but even after a longer lockup period, I do not or cannot just orgasm in this way. I would guess that everyone in or out of chastity, gets some degree of an erection, unless they are maybe a bit older, or have erectile type issues. (I am almost 50, and it has never slowed down at this point)
As for a cage, a cb6000 with the 3.5 inch tube is fairly roomy in comparison, and you can get a knockoff on Amazon for around 30 bucks. The manufacturer is charging way too much money for it, if you buy the name brand. It's a good beginner device, but for example, I am fairly well endowed and I can slide it off in the shower, with a bit of soap.
Some of this is dependent on your limits and what level of chastity you are interested in. I use a stainless device that can't be removed without the key, but doesn't completely restrict the ability to, as mentioned, feel vibration through it. I prefer to give full lock and key control to my fiance, or Goddess as I refer to Her, but not everyone is ready for that step.
In closing, I would tell you that for all of us, adjusting to the device in the first few weeks, is an up and down experience, with physical and emotional highs and lows. It took some time, but I learned to understand how to deal with morning or nocturnal erections, rather than trying to stop them or get out of chastity as a result of them. I succeeded at times, and I failed at times in the learning process, but learned to push through, mostly because it equates to a lifetime fantasy fulfillment for me. That need to act it out, moreso than a heavy reliance on my keyholder, drove me to adapt and learn to do it better. My KH provided the resistance to not take it off from the other side, permissably, but not always to my liking.
There's a lot more to this than just putting it on, and taking it off. That's chastity play, versus permanent chastisement, which can be fun in planned situations and small doses. Only you can say what you want from this experience, then work backward from there in setting up reasonable parameters for yourself.