These are examples to start from: change the amounts, rates and countries to suit your store. They use Automatic discount, so remember to switch from the default Discount code if that's what you want.
Condition: Cart total Is at least 100
Discount setup: Shipping → All shipping rates → Free
Condition: Cart total Is at least 150
Discount setup: Shipping → Cheapest shipping rate → Fixed Amount Off 25
If the cheapest rate costs less than $25, it becomes free. Other rates stay full price.
Condition: Cart total Is at least 100
Discount setup: Shipping → Choose specific rates → select your standard rate from the list → Free

If your standard rate's name changes at checkout (some carrier rates do), type "Standard" instead and choose Add "Standard" (wildcard match).
Or use All shipping rates and tick Exclude rates over a certain amount. This filters by price, so it only works while express always costs more than standard. Live carrier rates change with weight and distance, so choosing your standard rate by name is more reliable.
More options: How to offer free shipping on standard shipping only, not express.
Condition: Cart total Is at least 50
Discount setup: Shipping → All shipping rates → Fixed Price 5
Create two separate discounts:
Cart total Is at least 50 → Fixed Amount Off 10
Cart total Is at least 100 → Free
A customer over $100 qualifies for both, and Shopify gives them the free one.
Rule group 1: Customer tag Contains VIP
OR Rule group 2: Cart total Is at least 100
Discount setup: All shipping rates → Free
VIPs must be signed in at checkout.
Conditions: Shipping country Is one of Australia, AND Cart total Is at least 100
Condition: Postcode / ZIP Matches any of 2000:2050
Discount setup: Local delivery → Free
Condition: Cost of items from collection (total) Is at least 100, collection "Olive Oils"
Only olive oils count toward the $100.

Condition: Product collection Contains (any) "Bulky Goods"
Discount setup: All shipping rates → Free
Conditions: Cart total Is at least 100, AND Product collection Does not contain "Oversized"
Discount setup: Shipping → All shipping rates → Free
Conditions: Cart total Is at least 100, AND Cart weight Is at most 20 kg
Discount setup: Shipping → All shipping rates → Free
Choose kg before entering the weight. It defaults to grams.