The costs depend on your life style. If you are actively cruising they can be minimal because you will be anchoring out most of the time. Sail has the advantages of long range, (although many sailors put plenty of engine hours on their boats)--for 41,000 miles, Calif to Maine, to Florida, to Med, Baltic, Canaries, Caribbean and to Calif we ran the engine about 4,000 hours--but ocean crossings and even med crossing was under sail 100%.
Coming up the West Coast is mostly power--down is usually sail, but one time we went Long beach to La Paz--zero wind.
Roger's estimates are very valid. Sail boats have the cost of sails, and with care you can get 50,000miles out of a set. Rigging needs to be replaced at about 10 years etc. But systems have to be maintained. For example water pumps, generators windings, windlass motors, etc. These are intangiables. 10% of the cost of the boat is close to average.
However finding a good boat is a real problem. We just came back from S. Florida looking at over 60 boats and only found one which was suitable from my mini survey standpoint (deck rot, delamination, water intrusion etc were the main problems we saw in used trawlers). Sail boats have some slightly different problems. Get a very good Marine surveyor to look at what ever boat you buy., I would also suggest a buyer's broker, who is good. We have been working with a really great one for Florida. They are also hard to come by.
In the mid 80's our expenses were $1000 a month, for our living costs and boat maintance. This was a 62 foot lOA sailboat, but everything was new when we started, so the repairs were minimal, and we did all of our own work. Today, I would say that you can cruise for $2000 a month, if you are very careful about using marinas, and where you might eat out etc. But again, it depends on the condition of the boat when you start.
Going West from Calif. is a bit of a leap, and I would suggest that you spend at least a year cruising the Calif. coast (or where ever) before you leap off. This allows you to find problems with the boat, as well as hone your skills. It will also allow you to see if you are really suited for this life. There are lots of sail boats in remote down wind places for sale cheap--shattered dreams. We tracked two dozen boats in 1982 which had the same goals we had--basically a prolonged voyage, with specific destination leaving the West Coast. Several of these were lost in the Cabo Storm of Dec 1982. There were 4 divorces, 3 boats sank--in other places, and all of the crew containued sailing--but one took 15 years to complete the circumnavigation. The majority of the boats gave up in about one to 2 years and sold the boat where it was--at a loss.
If you are looking at a power boat, there are only a few trawlers capable of going West, and these are probably not limited budget boats--consider Nordhavn, Kadey Krogen, Defever Long Range Cruisers, Willards etc---boats built for offshore use, and long range.
I would be happy to answer specific questions. i consider one of the best long distance cruising boats to be the Cal 46, and these are available for $50,000 on up to the low $100,000, if well restored. These have enough power to go over 1500 miles under power (some over 3000 miles) --will power at 8 knots, 6 knots a gallon an hour, and sail at 8 knots in a stiff breeze on a reach. Many have circumnavigated or at least crossed several oceans. But they are close to 40 years old now and many require extensive upgrades. The pilot house type of sail boat is far better suited to long voyages, especially in higher lattitudes.