ROAD LEGAL TYRES FOR 87 KX500/ADVICE AND SUGGESTIONS APPRECIATED

[streetsleeper]

Hallo to all,
Just need some help please.
Those of you who are administrators or who visit the site regularly will remember me. I'm the new boi from England (not the newbie from New England!). Anyway, if you recall I'm living in Mexico north of Mexico City. Getting parts has been a problem as many people aren't prepared to send stuff here (understandably so). A friend with a Motorcycle Repair Shop has offered to get stuff sent here for me as he's always getting parts from the US, so that'll be OK in the future.
I bought the bike in September 2018 and it has a registration plate from Guerrero State (Warrior State) but this expires after 1 year and so I shall have to reregister it. The good thing is the bike is an '87 and over 30 years of age, which means I can register it as a Vehiculo Antiguo (obvious really but it just means it's an old vehicle i.e. classic motorbike) which means I can use it in it's original state without indicators etc. - I'm not sure of all the rules and may join the classic bike club to get more info.
What I do really need is some info on tyres for road use (the city is pretty d**n big by English standards and has over 2 million residents).
Presently: The front rim is Takasago J21 X 1.60 DOT 311 Japan 686 (IS THIS AN ORIGINAL PART PLEASE?)
Presently: The front tyre is (NOT FOR HIGHWAY USE) NITTO (Made in Japan) 3.25 x 21
Presently: The rear rim has NOTHING written on it (DOES THIS SOUND ORIGINAL PLEASE? ALSO DID U.S. AND EUROPEAN KX500s USE DIFFERENT SIZED RIMS?)
Presently: The rear tyre is CHENG SHIN (Made in Taiwan) 5.30-18 (presumably was okay for road use)
I would really appreciate advice/suggestions for a pair of road use tyres, both types please: road legal knobblies as well as ordinary road tyres. I do not buy Chinese stuff and prefer tried and trusted manufacturers: Michelin, Avon, Dunlop, Pirelli etc
In the photo you can see state of front tyre - the knobbies are actually coming off the tyre, and the rear is worse.
Thanks in advance for any replies. If I can get this bike to where I want it I am going to ride it up to the States and blog about my journey, to be followed by a proper book (I'm a writer).  

[umberto]

The original rims would have been DID, which should be stamped in the rim side.  It looks like you might have an upgraded front.  If the back doesn't have anything stamped on it, it may be a mystery wheel.

The tire sizes you listed are a bit old, so you will want to look for the metric equivalent.  The front will be an 80/100/21, and the rear will be a 110/100/18.  The first number is the width in millimeters, the second is the ratio of the width to the sidewall in percentage, and the last is the size of the rim it mounts on. 

Rocky Mountain has some good reviews on the Kenda K760 Trakmaster II tires:

Rear:
https://www.rockymountainatvmc.com/tires-and-wheels/kenda-k760-trakmaster-ii-rear-tire-p

Front:
https://www.rockymountainatvmc.com/tires-and-wheels/kenda-k760-trakmaster-ii-front-tire-p

The rear is $52.88, and the front is $45.88, which is a fantastic price for tires. 

[streetsleeper]

The original rims would have been DID, which should be stamped in the rim side.  It looks like you might have an upgraded front.  If the back doesn't have anything stamped on it, it may be a mystery wheel.

The tire sizes you listed are a bit old, so you will want to look for the metric equivalent.  The front will be an 80/100/21, and the rear will be a 110/100/18.  The first number is the width in millimeters, the second is the ratio of the width to the sidewall in percentage, and the last is the size of the rim it mounts on. 

Rocky Mountain has some good reviews on the Kenda K760 Trakmaster II tires:

Rear:
https://www.rockymountainatvmc.com/tires-and-wheels/kenda-k760-trakmaster-ii-rear-tire-p

Front:
https://www.rockymountainatvmc.com/tires-and-wheels/kenda-k760-trakmaster-ii-front-tire-p

The rear is $52.88, and the front is $45.88, which is a fantastic price for tires. 

Dear Umberto,
thank you for your swift reply. I have since found that the rear wheel is also stamped with Takasago J18 X 2.15 DOT 311 JAPAN 686 (That was my girlfriend's fault, bless her, I asked her to read what was written on the rim but she probably didn't want to break a finger nail rubbing off the dust.) I now actually reckon these are OEM wheels because they seem to crop up all over the internet in relation to KX500s. It appears that Takasago also sell EXCEL rims as aftermarket parts for different bikes.
It's my fault, I should have known better and done some more homework, but it's nice to know (I'm pretty sure) these were OEM.

I do actually know about rim and tyre sizes etc., as I'm an auto engineer (hahaha - read mechanic!) by trade and even worked in a tyre fitters, where that's all we did, plus balancing, tracking etc. Classic Minis were the most difficult to change, but you'd be amazed at the amount of fitters who don't know how to use and calibrate the machinery properly. I reckon every car that went out of the shop - sorry to say this, but the exceptions were the ones I worked on - had incorrectly balanced wheels and tyres and had their tracking all messed up. I say this as a warning to anyone who goes to get new tyres on their car and pays for tracking and balancing - it's not the machinery that's at fault, it's the idiots who don't have the mental capacity to analyse the data.

I shall definitely be looking up those Kenda tyres if they're road legal - I just wondered if anyone had fitted road legal knobblies to these 21" and 18" rims, or actual road tyres because that is what will be required. Even (some of) the cops here can read "Not For Highway Use" so I shan't be flouting the law.

Thank you once again. It's such a pleasure to have people like yourselves willing to help.