I was looking through tapped out for a budged deck yesterday and this is the one that I decided on using. I didn't have all of the cards you used but I was able to fill it in with cards lying around that were out of the super budget stuff lying around and the rest of the empty slots I was able to get for a under $10, very happy with the concept here.

One thing that new players should note, which I assume budget decks attract, is that if you flicker a creature (i.e. use a spell such as Turn to Mist on it), the spell you cast to make the creature flicker will still be on the stack when the creature's enter the battlefield trigger has to choose something. So for instance, when you cast Turn to Mist on Archaeomancer, you cannot choose to immediatly return Turn to Mist to your hand, it has to be something already in your graveyard.

Some alternative budget suggestions anyone reading this list might want to consider, if they already have them for example, are:
Pierce Strider can fill the same role that the chalice fills while still using the same flicker cards that the infinite mana generator uses.
Stern Proctor is some light artifact/enchantment hate. This deck seemed to be very light on artifact hate, so it needs something. Once you have infinite mana it might also be used to bounce your own Chalice/Strider to hand for victory.
Skyscanner is half a Mulldrifter for 3 mana, not a bad pick.
Think Twice is an alright draw card that Scrivener can get back or can be used in response to grave hate.
Pondering Mage is a decent effect with a 3/4 body.
Jester's Scepter could be put in as a second chalice: just flicker it a bunch and exile your opponent's libraries.
Azorius Chancery is a tap land and I generally don't encourage these, but if you are going for infinite mana combo via untapping lands, it can't hurt to had lands which can make extra mana. Also consider Temple of the False God if you take this route.
Sunscorched Desert can in fact win if the Chalice route is used since Ghostly Flicker is able to target lands.
Engulf the Shore is a decent boardwipe that could also be used to return your own creatures to your hand for value.
Time Wipe is a good boardwipe, especially if you are able to say, bounce something to recur your Breath of Life.
Sapphire Charm is also a second avenue to win the game via decking our your opponents. You choose the first mode and they get 100 or so draw 1 triggers during the next player's turn. Since the charm is an instant, it makes it possible to do the flicker combo on the end step before your turn so that, hopefully, your opponents have used up enough mana so that they can't do anything with the cards they draw on your upkeep; the draw triggers are one at a time so the opponents could respond to each one.

Also here are some upgrade suggestions of cards that are currently $2 or less, these are some of the cards I had lying around, for people willing to spend a bit more:
Library of Leng since you have the potential to draw a lot of cards in this deck, it's always nice to not worry about discarding them.
Star Compass this common is annoyingly expensive for it's effect: probably due to the diamond cycle being about double the price.
Flood of Tears isn't too bad since you get an etb right away. The next three should be considered as a unit:
High Tide can make the Drake produce 10 mana when it untaps only 5 lands.
Capsize will let you make infinite mana off of the Drake if you have at least 2 islands out and have cast high tide.
Cloud of Faeries is something that might work to combo off with if you are able to cast high tide multiple times in one turn. That's just a consideration here since I have yet to play test this deck against real players.

Looks like I made a mistake. I was a bit confused on triggered abilities and it looks like you can get the spell back that you used to flicker Archaeomancer or similar back. Nobody gets priority while a spell is resolving so once you do get priority and put the "return target spell from graveyard to hand" trigger onto the stack, that spell is in the grave at that point. My bad. It was even in a ruling to Archaeomancer, should have looked there first.

Thanks for the suggestions PaulMuadDib! I have some thoughts about your suggestions so I'll go through them step by step.

Pierce Strider/Jester's Scepter/Sapphire Charm: Once you have the combo, you should have access to your entire deck. Running cards for the explixit purpose of winning the game means that you are always running the risk of drawing a completely dead card. All current listed win-cons are both good as stand-alone cards but they also have the potential to provide a win-con later.

Skyscanner/Pondering Mage: These cards were previosly in the deck, but I took them out for separete reasons. Skyscanner was cut since most of or flicker/blink cards are single-target and single-use which means, just drawing a card proved to be to inefficient. The exclusion of Pondering Mage was because paying 5 mana for a Ponder was suppremely inefficient and the value that the ponder gained you was lost in how much mana it cost.

Stern Proctor: You are correct that the list is lacking in artifact hate and Stern Proctor might be warranted.

Think Twice: This suggestion I don't get. It is almost never going to be worth returning compared to other blink spells and it doesn't function like a win-con later, unlike Deep Analysis.

Engulf the Shore: You can reasonably expect to have between 2-3 per game. Thusly, this is going to function rather poorly as a boardwipe in the deck.

Azorius Chancery/Sunscorched Desert/Time Wipe: These I simply didn't think of. Especially Sunscorched Desert. They are all going in!

Again, thanks for the suggestions!

akselodd thanks for replying. And I'm glad you liked many of the suggestions! I always like to have redundancy when running a combo deck. I have run into decks with enough disruption that while I could make infinite mana, my one or two outlets were removed and I lost. Different ideas that way I suppose.

I suppose I was hyping up Think Twice a bit too much. It's just a filler that is coming out later. Not a bad card but I think Sapphire Charm probably out does in this type of deck.

One more consideration that I stumbled upon while looking through some cards today: AEthermage's Touch. This deck can't manipulate the top of the library (such as with a Brainstorm or other budget ones) but I think casting it enough times might let you get Peregrine Drake out for 4 mana or any of those big CMC creatures for possibly 3 or 4 less mana. Also if you have a flicker spell in hand, you can avoid the downside of the card.

A final thought here could be to run a clone or two, but not sure how useful that would end up being.

Oh one last boardwipe that you might have forgotten about and is very relevant to this deck is Dawn. Since many of the important value creatures are under 3 power, this could be a one sided boardwipe and if you ever need to discard it to handsize or some other reason, it can return important cards to your hand, such as the drake or other value creatures. At least worth testing out.