Barbeque
A few resources
Kadano's thread - Tons of good info here. Learn it at your own pace.
MIOM - Neighborhood P's Guide to Marth/Sheik - Worth a read
Up Throw On Sheik
From Kadano's thread:
Upthrow takes 40 frames against her.
0-8% – 2-3 frame window for Sheik’s jump escape timing (cannot be buffered)
12% – 2 frame window
13% – 1 frame window
17% – 2 frame window
21% – 1 frame window
22-30% – utilt is guaranteed, you need to turn if she DIs behind you
35-41% – utilt is guaranteed on neutral DI only, otherwise it will whiff.
32-45% – If she DIs behind you, tipper fsmash will miss just barely (she needs to hit a one frame window for the jump to avoid it). If she DIs behind you or in front of you, short hop fair will tipper her if done frame perfect (dash 1 frame, jump for one frame, then input the fair).
29-57% – On neutral DI, short hop uair will always hit her.
50-70% – On neutral DI, full jump uair will always connect, you need to delay the uair by one frame every 6% or so.
70-86% – On neutral DI, full jump → second jump uair will always connect.
As you can see, up throw to up tilt will combo from 22% to possibly 41% dependent on DI. Think of this as your first window and memorize it. Your second window, from 32% to 45% (I've gotten it to work up to 54/55) the instant dash-jump rising F-air will combo if she DIs to either side of you, and if she does neutral DI the short up U-air will work until 70%. Use this to start your juggles. This is the meat of your punish game off of grabs so it just be practiced until you're consistent with it so you can build up damage on Sheik.
Juggling Tips
Juggling is tricky but Sheik lacks tools compared to others when it comes to returning to the ground vs. Marth. Like any other situation in Melee, you want to have a gameplan when you transition to a juggling phase so that you can maximize your damage, minimize their ability to recover, and most of all make it more likely that you'll take the stock. Marth, in my opinion, is a control-assassin type character that can convert huge punishes or stocks off of a single good up throw with the correct gameplan.
Upon beginning a juggle, take note of whether or not they have their jump. Sheik's mid-air jump is really good, so you want to pressure her into using, but not in a way that you can't follow up on. A good rule-of-thumb is to never full hop to try and catch a falling Sheik unless you know for sure you can combo with it. This means at higher percents after connecting with U-air, use a series of empty short hops and swings to mix-up and fake-out the Sheik to trap them into landing into your sword. Your most viable moves in that regard are U-air, U-tilt and finally F-air. The first two are used to push Sheik back up into the air to prolong the juggle and rack up damage, while F-air can be used as a finisher to swat her offstage or catch her drifting too far away with the tipper hitbox that knocks her further upward.
Finishing your juggle can be done in a few different ways. The way I mentioned before, swatting her offstage with F-air is nice because it's not as punishable if you whiff and transitions you into edgeguarding. The other way, using a big hit like F-smash, is harder to pull off but with a larger reward. It's usually done by utilizing platforms and working it into a true combo. With enough raw damage, tipper U-tilt can finish the juggle simply by killing her off the top. Another possible finisher is N-air, but only on the second hit and its disjoint is a lot worse which can lead to you getting hit in retaliation.
Sheik will try to reach the ground usually by knocking you out of the air with one of her aerials. D-air and B-air have hitboxes that reach a fairly good distance beneath her falling body rather abruptly, which is why you should resist the urge to try and meet her in the air with a full jump. N-air comes out fast and shrinks her body a bit as it pulls her legs up in a more narrow shape, which can make you whiff while she falls through you with the lasting hitbox. F-air shouldn't hit you unless you find yourself beside her in the air, which you shouldn't be during a juggle. She can also airdodge through your attack and land before you if you commit too far with a jump. Despite all of this, proper anti-air can keep Sheik above you for a very long time.
Edgeguarding Sheik
Very frequently you'll find your punishes leading into edgeguard situations. The first rule to remember is that if Sheik cannot simply jump back onto the stage, you want to take the ledge and stall. You have two options for stalling: the high stall and the low stall. The high stall is done by jumping immediately upon releasing the ledge and then fastfalling back to catch it again. This puts your few vulnerable frames further upward, but you lose a bit of speed. The low stall is the most common and is done by simply dropping from the ledge and jumping back up to catch it. Your vulnerable body drifts a bit lower but has the advantage of being a few frames faster.
Choosing which stall option you want usually depends on where Sheik is coming from offstage. If she's high, there's a bit of a risk that she might hit you with a needle if you do low stall, which will really ruin your day. Doing high stall can keep you out of harms way for long enough for Sheik to fall low or choose to Up-B early. If Sheik is closer to the stage and coming from a lower position, low stalling can get you hit with her Up-B or even an aerial out of mid-air jump. High stalling can lose you the edge if you're not quick enough. Get accustomed to the different situations here so that you know when and how to stall. Doing so correctly will force Sheik to Up-B.
If you are below 100%, press forward while hanging from the ledge the moment you hear her poof. This will block her attempt to catch the ledge, and if she elects to reappear above the ledge, you have time to punish it on reaction. Otherwise, she will land onstage with her recovery and be caught in a very long endlag animation, which is a free punish. You can usually line up a tipper F-smash to knock her back off or finish the stock. The exceptions are if you don't have enough time (coming back on stage while above 100% requires you to ledge dash and can make it harder to line up the F-smash) or if she lands on a platform above you on Dreamland. Look for tippers first, otherwise go for reverse Up-B. You can ledgedash on stage, dash through her, then dash back at her and reverse Up-B all in a very short time. I believe this is also better for Dreamland since you can simply get back on stage and jump up to hit her with it very quickly.
Repeat as necessary. Be careful with center hit F-smashes because good Sheiks can amsah tech it and punish you. Reverse Up-B is also amsah techable but if done quickly enough they won't have had time to move their stick to the right position after having to choose their recovery angle.
Stages
FoD and Dreamland are the worst for this matchup, but with FoD being only slightly bad. Yoshi's is likely your best choice because of the earlier kill potential and good platforms so it's worthwhile to counterpick here. Second best counterpick comes down to your preference of platforms. I personally love Battlefield vs. Sheik because of the lack of walls for her to use for walljumps.
Platforms make juggles lead to deadlier punishes more often, but also makes it easier for Sheik to escape. FD will let you keep Sheik above you for the longest time, while making your ability to convert slightly worse. Stadium is a bit odd because of transformations. I like to avoid it, but it's all mostly up to preference/playstyle. Hone your own playstyle and figure out which works best for you, but in general: Yoshi's > Battlefield = FD > Stadium > FoD > Dreamland