Up front? Generator. $500 gets you a 2Kw inverter generator that will feed that load for about 3 gallons a night, so a week of fuel with that load $5/gal * 3gal/day * 7days = $105 + $500 generator = about $600 for a week of generator easily running your 1Kw load for a week.
Occasional/emergency use? Generator. If you're only spending a $25 for a jug of gas and it lasts a year, that's pretty cheap.
Long term constant utilization? Solar. The cost of gas will add up but it's going to take time to reach parity. If you plan your system well, can use used cheaper panels, etc. then it will break even quicker but when you've got your system specced and built right it should only be a few years.