Wormholes

Orcas, battlecruiser swarms, battleships, freighters, dreadnaughts, industrials, carriers, heavy interdictiors, or anything built buy Amarr.

According to http://wiki.eveonline.com/en/wiki/Wormholes#Wormhole_Identification C1 system wormholes seem have a total mass of 500Gg (giga...something,o maybe gigaton?), with a max jump weight of 20Gg. Except for Z971 which a total mass of 100Gg. Not sure about these numbers, but you could try to test the Z971 by jumping a couple of BCs through. As for ships, I'd use shield ships with a maximum mass of 15GT, which allows you to use 10MN ABs to fiddle alittle with the weight. The Naga fits nicely. You'd want a ship as close to 15GT as possible, but not above. Using plated cruiser, haulers, T2/T3 cruisers or even mining barges/exhumers could work, as long as the weight isn't above 20GT, or 15GT if you want to use the ABs to modify the jumps.
Atleast for the Z971 wormhole, using 3 Nagas would be ideal, just jump them through with 1 of them burning its ABs. That should make for a reduction of exactly 50%, which should show you it which way the random weight lays (if it supports up 10% more mass or down to 10% less. If it's above 50%, jump through with all Nagas burnings their ABs. If it's below 50%, jump with 2 Nagas with their ABs off and lastly with a Naga with its AB on.

For the other holes, the above guidance would work the same way, with either 5 times as many ships, 5 times as many jumps or a combination of ships and jumps.

If you've got an industrial op, you might be better spent in a C3 wtih a 5 bil static exit to high. The roaming connections are generally 2 bil and a lot easier to close, plus the static high can take a lot of abuse.

The thing I've seen used to crash a C1 hole before is the Impel, which can get just under the single-jump mass limit. Still, crashing C1 holes is only marginally less tedious than mining, they have a stupid amount of mass to take off in such tiny bites.

As other posters have said, get a ship that's as close to 20 Gg as possible without going over. Retrievers are right at 20, but you might run into pvp while hole-collapsing, and you're dead if you're in a retriever. I use a Drake with a 10MN MWD, for 14.8 or 19.8 Gg. Pre-Odyssey I'd also use a Talos, but I believe those don't fit anymore, and you'll need to use a Naga.

A destroyer with a 10MN AB is also useful to have for collapsing incomings from k-space.

C1 statics are 1000 Gg total, incomings from other w-space are 500 Gg, incomings from k-space are 100 Gg. If you're solo and have no alt accounts, collapsing statics is a waste of time (you need 25 round trips on average, so you're looking at about 2 hours of nothing but going back and forth). Incomings from other w-space are doable solo but take forever. Incomings from k-space are easy, you just have to keep track of how much you've done.

If you have multiple alt accounts, it gets easier. I collapse with three accounts, takes ~20 minutes for incomings from w-space.

For ending up on the right side...make a spreadsheet, keep track of how much you've sent through and what the min/max reminaing is. When the hole switches to 50% or 10% mass, you can update your min/max estimates. By varying the mass you send through via the MWD/AB, you can easily put the hole in a state where you collapse it while you're on the right side. I've collapsed a lot of C1s, and only ended up on the wrong side once.

A HIC is certainly useful to have, but has anyone actually seen a confirmed >10% away from nominal mass hole? I've closed probably more than a hundred C1s, and never seen one that fell outside the 90%-110% range.

One of the mining ships does it pretty well. Forgot which.

OP is talking about C1 wormholes, so "mass of a battleship" isn't going to fit.

Still useful to have one with a 10MN prop mod.

Not in C1 space. I have seen a mass outlier (extra heavy) B274 though.

Not sure what you mean. You can't fit a ship with the mass of a battleship through a C1.

Sure, you can use a HIC for the last few passes to ensure you end up on the right side, but it's less efficient than other ships to use for the majority of the passes.