Angies List - Project Cost Info, Home > Electrical, and Home > Plumbing under Browse Projects at lower left have a number of previous similar questions but more in pieces - like move washer and dryer to new area but not the new electrical upgrade for instance, or electrical upgrade for garage power tools but not the washer and dryer.
Since you are talkiing just one washer and dryer, water lines should be good - though to avoid neighbors complaining about you pulling all the water from their units if your washer has high input capacity you should tap in as close to the water building entry point as feasible - and install a throttling ball or globe check valve (one designed to restrict flow continuously, rather than just turn off and on) in the inlet lines at the washer for possible throttling of the inflow rate is that happens. Won't hurt washer if inflow is throttled a bit - just takes it longer to fill each cycle. Same effect can also be achieved by reducing the pipe size at the washer, but that is not adjustable.
Check the required discharge line size from the washer - hopefully not over 3", though you should have no great trouble putting in a 4 inch discharge connection to the sewer main especially if a partly exposed run does not bother you - just make sure it has the legal drop before it turns to the line (should be no trouble with the required platform height), and that it does not tie into the main sewer line near another drain - plumber should know the rules. And definitely ask for a sweep wye entry to the sewer line, so it does not back up into the line during discharge as it can from a Tee.
The power, especially if going electric dryer (ouch $ in most areas), will need a dedicated circuit and breakers to it, and ditto to electric water heater. Depending on the existing breaker panel capacity, maybe able to tap in there. Otherwise, no big thing to put an additional tap at the meter area (normally in a disconnect or main breaker box right after or integral to the meter box) so you have a second tap feeding to your unit - but would run off same meter. Obviously would need electrical capacity check, but unless this is a pretty old unit or all-electric heat in the building, may need no upgrade to the service or meter because normal building wiring allows for electric water heating and washer/dryer - but not in all areas. There are some houses in very high electric cost areas with cheap natural gas which do not have provision or capacity for electric heating or drying.
If washer is going to be steam washer with internal steam generation (as oppoosed to higher-temp water heater dedicated to it) then that will put a quite substantial demand on the electrical system and may bump you up to more upgrades.
Generally, there is (for your purposes) generally no need for a new meter and usually they will not put a second meter on a single living unit unless it is zoned and permitted for a business or second residence unit (like mother-in-law apartment or such). Normally the electrician will just tap off the incoming line at/right after the meter to run a new lead the demand area (through the garage wall). Commonly you can run 3-5 feet from the tap point by code before you have to have a breaker box so that hopefully will get you into the garage, where they can put in a secondary breaker box for the 220/240V for the hot water heater and for the dryer, and 110V(unless going super powered) for the washer - and any other capaqcity for future garage outlets one might want to add in the future. (Once doing this, unless it bumps you into a larger service, it costs only $100 or $200 or so additional to provide extra capacity for future additional circuits off the secondary panel.
First thing would be a written evaluation by an electrician for the load demand, and whether your service has adequate amperage capacity (and whether main breakers and feeds from the meter will need upsizing), and whether coming off the existing breaker box is feasible or economic. He could give you a bid at the same time for the upgrade/new panel complete ready for your new appliances (have the specs on them ready for him).
Then a plumber estimate for the water lines and drain line connection - probably include the platform in his scope unless you are doing it, as you indicated. (Check on design - for that equipment, probably going to be about 2x8 frame with 4x4 legs (probably 6 rather than 4 if all on same platform) with back 2x8 lag to the wallfor stability, and I use 1" marine plywood (marine to resist rot for when you get leaks down the road) covered with nailed-down concrete backer board for waterproofing and fireproofing - though since not gas fired appliances that fire-resistant feature is not needed in your case.
Oh - and since you said deep garage and appliances going at the back, pay attention to not only the platform requirements, but also the protective bumper requirements. And theseismic tieback likely needed for the water heater. Some areas also require a lip on the platform so washer/dryer can't vibrateoff in earthquake or operation - a good idea - I just use a piece of 1/4 round.
When building platform consider where you want the water to flow in the event of leakage - probably not towards the back wall - I usually put trim around all edges with a gap in the front center.
Check the referenced links above - done the easy way with no hassles and no meter/service upgrade needed, I would guess you are in the $1000 range - pushing up into the $1500 range probably if no easy way to get at sewer line without cutting into slab. Your idea of going down outside the wall will work only if in a totally non-freezing area.
If your service needs upgrading from (and including) meter to main breaker or wherever the tap is made for the second breaker box, then into the $1000-2000 range probably. Should not get above that unless your service is near capacity and the utility has to upgrade the service drop (incoming supply line to your unit), and you need to upgrade meter base and main breaker/disconnect as well.
Realize these are REALLY broad ranges, depending on your existing situation and also on what local coderrequirements are, and if nay of your existing service is so old that it need upgrading to meet code as part of the upgrade - normally anything being upgraded or increased in capacity has to be upgraded to code - not entire system necessarily, but the components being modified or upgraded have to meet current code.
