Spades and hearts. Mixed stacks can hold cards in place, but only a same-suit run can travel or go home.

2-Suit Spider Solitaire: The Rules in Brief

Spider Solitaire with 2 suits uses the same rules as every version of Spider Solitaire. The cards are dealt into ten columns, plus a stock that deals one card onto every column, five times, but not while a column is empty (unless fewer than ten cards are left on the table). Any card can go on a card one rank higher, only a descending sequence of one suit moves as a group, and each complete King-to-Ace run of one suit is removed automatically. Complete all eight runs to win: four in spades and four in hearts.

What Changes with Two Suits

In the 1-suit game every card is a spade, so every build is in suit and any descending sequence can be moved. With hearts in the deck, that is no longer true. Take any 8 of spades: there are eight 7s that can be placed on it, but only four of them are spades.

You can still put a 7 of hearts on an 8 of spades. The two cards just become a mixed stack: they cannot move together, and they can never be part of the same finished run. Each place where a column switches suit is a joint that has to come apart before those cards can join a run. A column ending with the 10 of spades, 9 of hearts, 8 of spades and 7 of hearts has three joints and can only be moved one card at a time.

So 2-suit Spider is mostly about joints: making as few as you can, putting them where they do the least harm, and taking them apart whenever you get the chance.

2-Suit Spider Strategy

Build in suit whenever you have a choice. If a 7 of hearts could go on the 8 of spades or the 8 of hearts, choose the heart. If a tap sends your 7 to the wrong 8, use Undo and drag it instead.
Use off-suit builds to dig, not to store. Early on, putting a heart on a spade is often the only way to reach a face-down card, and that is fine. The trouble comes from piling a long stack on top of a joint, because those cards can only be moved off in same-suit pieces.
Keep long same-suit runs uncovered. Try not to put an off-suit card on the end of a long same-suit run. A 5 of hearts on a run of spades from the 9 down to the 6 pins all four spades in place until the 5 moves again.
Make repair moves as soon as they appear. If a 7 of hearts is sitting on an 8 of spades and an 8 of hearts becomes free, move the 7, along with any hearts in sequence on it, across to the 8 of hearts. One joint disappears and nothing is lost.
Break a same-suit run only for a clear gain. Splitting a run turns one movable group into two, so do it only to turn over a face-down card, empty a column, or extend a longer run of the same suit. For example, if one column holds only the King of spades down to the 5, and another ends with the 7, 6, 5, 4 and 3 of spades, moving the 4 and 3 onto the 5 brings the King's run two cards closer to completion.
Use empty columns to sort suits. Suppose one column ends with a 9 of spades and an 8 of hearts, and another ends with a 9 of hearts and an 8 of spades. Move the 8 of hearts into an empty column, put the 8 of spades on the 9 of spades, then move the 8 of hearts onto the 9 of hearts. Both pairs are now in suit, and the empty column is free again. The same trick moves mixed stacks: to shift a 9 of spades carrying the 8 and 7 of hearts onto a 10, put the two hearts in the empty column, move the 9, then bring the hearts back. With two empty columns you can move longer mixed stacks the same way.
Tidy up before every deal. Each deal drops a card on all ten columns, and most of them will not fit where they land. Before you deal, make every repair you can and turn over what you can. Then fill any empty column, since you cannot deal while one is open; a King and its run is usually the best choice.