Beta readers are worth their weight in gold. Make sure your story is as good as you can possibly make it yourself before sending it out to them. You waste their time as well as your own when they pick up issues you could have fixed yourself with one more edit.
Definitely spellcheck! There’s no excuse for spelling errors! Proper usage of homonyms (e.g. their, there, and they’re) is one thing spellcheckers will miss as well as simply typing the wrong word. We all tend to read right over them in our own work, but there’s no excuse for blatant garden-variety typos that a spellchecker should catch.
I have made this mistake before and had things pointed out that I planned to fix. My first draft tends primarily to be action and dialog, any imagery and emotion sometimes missing entirely, or more of the “tell” mode instead of the preferred “show.” I have learned to wait until I’ve really polished the story to my own satisfaction before handing it over to a critique group or beta reader. Bear in mind it is probably the only version of your story that they’ll ever read. Don’t you want it to be your best work?