The average number of proxies seems to be around 10 right now. Some tournies are 5 + $1 for each additional, which is pretty cool and adds to the prize pool, but I think most places are moving towards 10 as a standard.
As far as where to start in terms of card acquisition, you can go about it a couple of different intelligent ways.
Method 1) Choose a relatively inexpensive deck like Dredge, or a deck with many cards that overlap in other formats you try to play, and try to bang out those cards pretty quickly.
Analyze what a specific block of cards will cost you. With the
TK/ELD version of Dredge (with mana), for example, these cards can also be played in the Legacy and Extended versions (prices are what you should be paying on eBay if you're patient):
4 Ichorid - $10/playset
4 Bridge From Below - $12/playset
4 Narcomoeba - $2/playset
4 Stinkweed Imp - $2/playset
4 Golgari Grave-Troll - $6/playset
1 Cephalid Sage - $.50 each
1 Angel of Despair - $2 each
1 Flame-Kin Zealot - $.50 each
4 Careful Study - $2/playset
4 Breakthrough - $3/playset
3 Dread Return - $.75 each
4 Gemstone Mine - $12/playset
4 City of Brass - $10/playset
4 Cephalid Coliseum - $4/playset
SB: 4 Leyline of the Void - $30/playset
SB: 4 Chain of Vapor - $4/playset
SB: 3 Emerald Charm - $.50 each
SB: 4 Contagion - $.50 each
That's
US$105.75 for the core of the deck and sideboard, which is playable in 3 formats. Now you can add stuff to that, depending on what you want to sideboard like, and what you want to proxy:
1 Black Lotus - $650/PROXY
1 Ancestral Recall - $375/PROXY
1 Mox Sapphire - $350/PROXY
1 Lotus Petal - $1.50/PROXY
1 Lion's Eye Diamond - $10/PROXY
4 Bazaar of Baghdad - $640/playset/PROXY
So that's 9 proxies total, bringing you below the increasingly standard threshold of 10. If you want to invest more money (like for 4 Lion's Eye Diamonds, or $40 total), you could drop the deck into Legacy. You could also potentially spend $10 each on a few Pithing Needles if you chose to run that in your board.
Method 2) Acquire staples for the format when you can get true value. What I mean by this is, don't just go looking for cards you want, but rather acquire something
you'll actually use whenever you're getting good value. For example, if a set of 4 Flooded Strands regularly goes for $52/playset, and you can trade into a set for about $44, you buy them, because you're getting good value. Try to focus on picking up cards for value, and ones that are playable in other formats as well (increasing the likelihood their value will be buoyed by more playability); for example Dark Confidant, fetchlands, etc. This way, if you decide to scrap your plan for Vintage, you can trade out of the cards more easily, and retain value.
Welcome to Vintage.