Congratulations on your new doggie!
NO reason you can't take the dog to the park but keep the leash on!
You mentioned crate training but in what sense?
If you need to go out and are worried about leaving the dog free reign unsupervised then I would say yes try crate training. BUT
make it a happy thing. Put toys in there with some treats and water, make it really comfy with a blanket and such. Praise your dog to no end with all kinds of love and pats, this is a good time to get him to learn his new name...say good 'name' over and over again! They learn FAST!!
My last rescue learned her name in less then a week!! NO KIDDING!
Don't leave the dog too long in the crate at first, say 10/15 mins when you go to the corner store for bread or something. Then praise the dog when you return and go take him outside right AWAY!!
The next time you may wanna try leaving him OUT of the crate for the same amount of time, and when you return and things aren't destroyed praise him again and take him outside.
IF you return and something is destroyed/chewed on or the dog has gone to the w/r indoors. DO NOT scold the dog!! This will reinforce negative behaviour and the dog will at this time have no idea WHY it's getting negative attention. HOWEVER SOME dogs can figure it out, and no matter what type of attention they get, they THRIVE on the attention, if even they've done something destructive. SO do not give ANY attention to the issue that happened okay
Every time before you go out somewhere make sure you take the dog out to go to the w/r okay
this will make both of you very happy in the long run!
Normally dogs from shelters will follow you around a lot, they are in unfamiliar surroundings and are settling in, they wanna make sure that you aren't leaving them.
Remember they have to learn all about YOU just as you have to learn about THEM!
So you had a couple of accidents, big deal! Look to catch the dog peeing then take him right outside when he does.
However, the more frequently you take the dog out, the less likely to soil inside. ALSO remember this dog has been in a shelter and was accustomed to HAVING to go to the w/r indoors for who knows how many weeks/months.
Relax and give it time. Spend a LOT of time with your dog, show it love and attention as well as discipline.
Is this your first dog or first rescue?
As for the chewing, they normally do this when they are bored or want attention...so try to keep the dog active and busy. There are all kinds of toys and chewy things for this.
Many shelters are not accurate on the dogs age, this dog could be younger ... and still puppy'ish! It may have a lot of puppy stuff to go through yet.
So I say get some balls, a long lead, some treats and head over to the park to play!
Enjoy this time, you're gonna bond just wonderfully if you are consistent.
Congratulations and post up a picture of your new addition
Luba