Xantrex 1500 + Solar Panel - HOW?

It largerly depends on just how much power in terms of amp-hours is used from the batteries in a 24 hour period and how many 24 hour periods there might be without sunshine or utilities. The later is hard to predict so you may just have to pick a number.
What I like to do (this is all basic) when sizing a battery bank for an off grid system with all VAC (volts alternating current) loads from an inverter is to calculate the anticipated load as watt hours at 120 VAC for a 24 hour period, then turn that into amp hours at a nominal DC (direct current) voltage. I then multiply that times 5.
Once I know this I then size the PV (photovoltaic) array to replace one 24 hour period or 20% of the total battery capcity in one sunny day, preferably Dec. 21 - the shortest day of the year. For example:
In a 24 hour period 4,000 watthours is consumed at 120 VAC - at 24 VDC that is 167 amp hours, multiply that by 5 and we have a total battery capacity of 835 amp hours at 24 VDC. To replace with PV what is used in a 24 hour period just take the 4,000 watthours and divide by the "number of hours of equivilent full rated charge." Bear with me on this one. Goto
http://rredc.nrel.gov/solar/old_data/nsrdb/redbook/atlas/

and in section; 1. choose - minimum, 2. choose - December, 3. choose - flat plate tilted south at latitude + 15 degrees, 4. "view map." Once you have done this just pick the region in which you live and you can see the "number of hours of equivilent full rated charge" from a PV array. Become familiar with this calculator. Expieriment with the values and parameters. You will see on the maps legend kWh/m2/day, that translates into kiloWatthours per square meter per day. Now there is a lot of math involved in getting a more precise value from this in terms of the number of equivilent full rated charge hours from a PV array but to keep things simple I will just pick the number 2 from the legend. So now we know that we can expect about 2 kiloWatthours or 2000 watthours a day from a PV array on the shortest day and we will need 4 kiloWatthours or 4000 watthours to replace what has been used from the battery in a 24 hour period. Basically we will need a 2000 watt PV array at 24 VDC in this example. From there the charge controller and all of the subsequent electrical needs can be sized to meet the NEC (national electrical code) requirements. Again, this is all basic. If one desired to, one can calculated more precisely taking such things as inverter inefficiencies, the actual size in square meters of the PV array, wire lengths, etc., etc.. This list  could go on and on depending on how precise one wants to be.

Since you allready know the battery capacity in amphours simply translate that into kiloWatthours and use the map to figure the PV array size and subsequent electrical needs.

The size of the PV module depends on the frequency of usage. 60AH battery with only 20% discharge = 12AH capacity usage. A 15W PV-module (1A charge) is recharging in a few days, for daily usage of X1500 a > 50W module (3A charge)is needed.
If the X1500 is seldom used and can be easily recharged from AC at home, spending hundreds of US$ for a PV module to save a few cent's of AC recharge cost is not very economical.
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I am also suprised about the cost of X1500 including battery, cart + inverter together for 325$ compared with DR1512 inverter for 652$. However the DR1512 has an 165A charger compared to the 5Amp from X1500 and is made to run non-stop for years.