As long as you aren’t going too wide for your rim (I wouldn’t go more than double your rim width) a wider tire can add a bit of stability, but what is more noticeable is it’s ability to absorb more shock when landing, hitting lumps, cracks, etc.
Kenda makes good budget tires. Relatively tough and long lasting for a good price. What you don’t get is the subtle sidewalls and extra-grippy rubber of the premium brands. I have a white Kenda Kikzumbut tire on my 20" and feel it’s an excellent general use tire.
Another great budget conscious tire brand to look at is CST. I have heard good things about the cyclops.
Ironically the more expensive tires tend to wear out faster due to their stickier rubber compound.
That’s why I did it on my Avenir. The stock (Duro) tire was fine, but I was practicing with it on my brick patio and on my driveway, which has bumps and cracks. A wider tire meant I could run lower pressure, so that stuff didn’t disturb the unicycle as much as I it rolled over it.
I think the 1.95" wide tire sits on the Avenir rim very nicely. The rim is somewhere in the 1.25-1.375" range.
I just noticed btw that the tire I linked to above is out of stock. Sorry to have missed that. Unicycle.com does list whitewall and all-white versions of it in stock.
Another one that looks reasonable is the Kenda Kontact. I stuck one of those in an online shopping cart a while back to pad out an order where I was already going to pay shipping. I haven’t used it yet but it’s also 1.95" wide and will probably go on my Avenir when the current tire wears out. It comes in fun colors. Mine’s yellow.