Hey there,
I am a mostly casual player with a large interest in playing vintage eventually, so these "getting started" articles always interest me. I've been getting my hands on some vintage staples over the last couple of months (not specifically aimed at one deck/archetype though) like sol ring, academy, yawgmoth's will etc. and when I first read this deck I mostly agreed with the other comments made here. However, after giving the subject a little more thought, I think that this can actually be a good basis for a beginner's deck. Here are some comments on the choices you made:
Without further ado, here is "Budget Blue"
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12 Island* (0)
4 Terramorphic Expanse* (c)
4 Ghost Quarter (u)
1 Stripmine (u)
1 Lotus petal (u)
1 Sol ring [$9-13] (or just another island)
1 Mana Vault (u)
You already said that Terramorphic Expanse is bad in this deck, and the question is how important are the shuffle effects for this deck. I think that they could be exchanged for islands (or maybe keep 1 or 2), and add Merchant Scroll to the deck for more shuffling. It is slower to activate brainstorm with a merchant scroll shuffle than it is with a terramorphic expanse, but only by 1 mana, because the expanse's fetch comes into play tapped. On the other hand, they're basically free to get, so getting a playset is not a bad idea after all.
Mana Vault seems a bit odd given the mana cost of the cards in this deck, but a 2nd turn frozen aether or shackles activation might be worth it. In any case, it's a good card to own I think.
4 Brainstorm (u)
4 Ophidian + (r)
4 Ponder + (c)
I'm not completely sold on Ponder, because it can still force you to play with 1 or 2 bad draws down the line. There is too little brokenness in this deck to justify running a 1-mana, dig-3 card (which seems to be the reason why this is played). I think that changing out a few for Merchant Scrolls might be abetter idea. It's a true and tested vintage staple, and you can easily search for you bounce, or ancestral if you start proxying. Even now, you can use it to find shadow of doubt if you have a lot of ghost quarters out.
2 Sower of Temtation [$6-8]
2 Morphling [$12-16]
3 Back to Basics (r)
3 Frozen AEther (r)
This is the part with the most critisism, mainly because of Morphling's price tag to usability ratio outside of this deck. Might I suggest switching these for Meloku, the Clouded Mirror? She is a lot cheaper on the budget, I have seen her in some lists on these forums, and her land-returning ability has a nice synergy with Foil below.
As for Sower of Temptation, I'm not really sure if it's the best choice, and I think it's worth noting to people who seek to cut the budget of this deck even further that control magic can also be played in this slot. If your opponent has no creatures, then the Sower isn't worth casting anyway (4 mana for a 2 power beater). In addition, control magic is a bit safer in terms of removal. The question whether you'll use control magic outsideof this deck is just the same as for the sower, so I think it's a nice budget alternative that should be kept in mind.
4 Force of Will [$25-30]
2 Foil** (r)
2 Echoing Truth/Rushing River (maybe 1 and 1) (c)
3 Nix/Spellsnare*** (R/u)
3 Shadow of Doubt (r)
Force of Wills are a pain, and it's an investment that I still have to make. But as stated just about everywhere, if you want to play vintage, you'll just have to. Foil is a nice budget addition, and it allows some nice tweaks to the deck. Meloku, as I mentioned earlier, is one, but it is also a nice card to have when you want to play Gush. Gush is cheap to get, and is making quite an impact. In addition, it draws you extra card, including Islands you might not need that can be pitched to Foil (or shuffled away with Brainstorm). Effectively giving you more Force of Will for in the mid- to late game.
I have personally been testing Shadow of Doubt, as I really like the card. I must say that if you get to counter something with it, it's awesome (I haven't even thought about the synergy with Ghost Quarters). Other than that, it's never a truely dead card due to the cantrip effect. However, it can be hard to find the spare mana to cast it, which makes it dead for a few turns, which could prove fatal. Then again, I would definately suggest investing in them as they can be a nice surprise for people, and they aren't that expensive anyway.
Another counterspell you might want to look at for the metagame slots is disrupt. It also cantrips, which makes it good enough in my eyes, and it can stop early scrolls for ancestral. It's also quite good against ritual effects, as it can turn their mana calculations upside down, and draw you a card as well.
==== Sideboard ========
4 Energy Flux (u)
4 Serandib Efreets ($4-$6 for green-frame revised)
3 Vedalken Shackles
4 Hydroblast/BEB // or Propaganda (u)
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I don't have any sideboard experiences, so I can't really comment on this. If you have trouble casting Energy Flux, then switching some for Hurkyl's Recall might just do the trick (they shouldn't be too expensive, and can be used in sideboards in future decks as well).
The Serendib Efreets seem a bit odd and pricey as well. I have no idea what else to put in these slots though.
EDIT: How is Leyline of the Void instead of Serendib Efreet? It's a widely used card and shouldn't cost any more than the efreets. In addition, with the hybrid mana on shadow of doubt, and the power/cheapness of duress (which anyone should also get a playset of), it can be a good starting point to add black mana to the deck in the form of Polluted Delta / Underground sea, giving you some sort of longer term plan to expand this deck with some more solid vintage staples that you are pretty much garantueed to use in the future.
Nice read, keep up the good work!