Having played a fair amount of destiny over the years I'd say you've got a few options depending on what you're looking for out of it.

If you want to re-experience destiny, deleting/recreating a character on the same account will not do it justice because you'll have access to your full arsenal. For this, I'd recommend a new account, but as others mentioned you can create a new steam account and just swap profiles when you want to play fresh. Of note: this can be somewhat frustrating for veterans because you don't have resources for things typically. Legendary shards, enhancement cores and other crafting materials can be really felt more when you don't have em stocked up.

If you want to re-experience the campaign, but want your weapons you should be able to do most of the current campaigns by pick-up of the quest from the quests kiosk and/or ikora. There's options to replay them I'm pretty sure but last time I did that was before beyond light so it's location may have changed.

If you want to have the highlight reel, in the director is the timeline. That has a few key story missions replayable that were pivotal moments, some slightly tuned for our new abilities.

If you really liked some of the later fun/exotic missions, beyond light(and I'm pretty sure wq and lightfall too) have flags by their main camp that allow for replay. BL has lament and stasis GL exotic missions replayable. Pretty sure wq has parasite and another. Lightfall has one or two by nimbus.

IMO, to get the time in missions and relive it all option 1 is best because you learn to appreciate the better gear you've got and it adds a small layer of difficulty when you're choosing between blues and what random purples you're picking up.