Lego Classics alternative
Lego bricks can be purchased individually from Lego.com using their Pick-A-Brick service.  

https://www.lego.com/en-us/page/static/pick-a-brick?icmp=HP-SHQL-EG-NO-pick-a-120  

If you have an official Lego Store near you then buying bricks from their Pick-A-Brick Wall is a less expensive option once you figure out how to maximize the amount of bricks you can stuff into a cup.  

There are also sites that sell individual bricks, often at a lower price:  

Brickset: https://brickset.com/

Brickowl: https://www.brickowl.com/

You may also be able to find good deals on Ebay for bulk bricks already sorted by color and type.  

https://www.ebay.com/sch/i.html?_from=R40&amp;_trksid=p2380057.m570.l1313.TR6.TRC1.A0.H0.Xlego+bulk+bricks.TRS0&amp;_nkw=lego+bulk+bricks&amp;_sacat=0  

I would recommend buying one starter set of basic bricks to compliment the basic bricks and provide them with some variety.  Sets like 10717 have minimal amounts of special pieces compared to other.  

  

They have made sets in the past with a lot of basic bricks, many of them were sold under "Educational &amp; Dacta".  One of the more recent releases was set# 45811 that looks like sells for around $40.00 on Bricklink.