Haven't been playing Vintage for more than a few months. Tried some different decks and I find myself really enjoying this mono-blue control contraption. I used to play Legacy and me and my buddy always wanted to play Back to Basics and Propaganda, but it never worked in Legacy. I got in to Vintage and it doesn't seem too terrible.
I haven't had too excessive of an issue beating Dredge, Storm, Oath, or Pyro/Mentor decks. I usually have game against goofy brews. The main issue is my Shops match needs to get better.
As it stands, I need a pretty stellar opener to beat them.
Here is the deck list (not sure how to make it so the pictures come up, probably something to do with [ and ] but I'm not 100% certain)

Main Deck

10 Island
4 Polluted Delta
1 Library of Alexandria
1 Strip Mine

1 Black Lotus
1 Mox Sapphire
1 Mox Jet
1 Mox Pearl
1 Mox Ruby
1 Mox Emerald
1 Sol Ring

1 The Tabernacle at Pendrell Vale
2 Propaganda
1 Null Rod
2 Back to Basics

4 Force of Will
3 Mental Misstep
2 Flusterstorm
2 Mana Drain

1 Ancestral Recall
1 Brainstorm
1Ponder
1 Preordain
1 Time Walk
1 Treasure Cruise
1 Dig Through Time
1 Gush
3 Mystic Remora
4 Repeal

1 Magus of the Future (trying this in place of Gush #2)
2 Vendilion Clique
2 Jace, the Mind Sculptor

Sideboard

4 Grafdigger's Cage
2 Ravenous Trap
2 Echoing Truth
2 Engineered Explosives
2 Steel Sabotage
2 Hurkyl's Recall
1 Energy Flux

I am not opposed to adding a small splash if it will improve my Workshops matchup
I wasn't sure if maybe the veterans of the format would know of some secret tech to assist a newbie with the mud monster.

Thanks in advance!

i've been crushing shops online with mono blue.

sideboard steel sabotage plus annul, it's not even fair, you don't run 4 drains, which is an issue.

thirst for knowledge is a better draw engine, 3 jace, 2 tezzeret, vault key, blightsteel.
i've tried back to basics, it doesn't do enough, i found myself rather drawing cards and comboing out

This is just a first pass, but basically, you want more lands and don't want to lose to a turn 1 Lodestone Golem.

If I were starting from that list I might try:

-2 propaganda,
-3 mental misstep
-2 flusterstorm
-3 mystic remora
-4 repeal
-1 magus of the future

In a mono blue deck:
+3 lands
+4 Sculpting Steel
+3 hurkyl's Recall
+3 energy flux
+2 ??? (Annuls?)

or with a red splash
+3 lands
+4 Ingot Chewer
+2 Dack Fayden
+2 Energy Flux
+4 ??? (EE? Sabotage?)

or with a green splash
+3 lands
+4 nature's claim
+2 trygon predator
+2 Energy Flux
+2 ??? (EE? Sabotage?)

That's a post-board plan, so I don't know how those cards would be split up between maindeck and sideboard. For a splash in this deck (with B2B) I'm guessing you'd want 1 basic and 2ish duals. Normally I'm not a huge fan of Energy Flux, but Energy Flux + Back to Basics is just too fun to pass up

Some kind of mono blue should be pretty good against shops. I think the bigger problem is Mentor, where their Gushes basically blank your Back to Basics. This is why people moved to Blood Moon and run it in a U/R shell. Both back to basics and blood moon pretty much shut down dredge and shops; which is a really strong place to be pre-board. Blood Moon is probably a little better against mentor and it puts you in Red so you can run lightning bolt or sudden shock, as well as good anti-shops cards.

I totally agree with mmcgeach about some 2 color blend because it will help against Gush. As for the shops match up, all I can say is high land count and then Energy Flux. Slow shops builds just can't win against Flux, and pretty much can't remove it. The exception is the really aggro shops builds, but with the restriction of lodestone golem I would imagine that those builds will fade out in favor of slower, more controlly versions that flux will just crush. If you have a lot of lands and a lot of basics, you can wait out spheres and tanglewires and just drop a flux. (Against some builds I will just go mox mox land turn one and drop the Flux, cause the other guy just scoops.) (Also, if you are just starting out I would recommned using mtgtop8 a lot because it lets you metagame and see what decks you should be planning for.)

On the Gush topic, I have only played against Gush decks a handful of times but it has been a favorable matchup. Generally they are casting a bunch of spells, which Remora loves or they are waiting and I keep making land drops and holding cards for countering their few key threats. The times they have landed a token producer I have generally been able to thwart it with Propaganda or The Tabernacle. The Engineered Explosives were put in the board to help with the tokens but also along with a mox wipe up spheres
I am open to the idea that my sample size is too small and what I see as a favorable matchup is in reality a poor one.

The idea of a red splash is appearling. Blood Moon serving a very similar role to Back to Basics while also opening up some other options.

With the new B&R list, perhaps not much will need to be changed.

Thanks for the replies!

Shops really shouldn't be much of an issue now post Golem restriction...

@themonadnomad I would be baffled if that actually turned out to be true.

@Aaron-Patten Really? Baffled how? I can't see it really locking a blue player out of the game the way it once did...

@themonadnomad I think it still can but probably doesn't absolutely have to completely lock the opponent out in order to win the game before an opponent without 4 Mishra's Workshop can. The deck was still a powerhouse before the printing of Lodestone Golem, it's just a matter of finding some different tools now.