If you will be using any large stationary power tools, or even high amperage portable power tools (like routers shop vacs, air compressors) for extended periods, use dust collection or, especially, if you use electric heating or air conditioning then it really is not especially practical unless you have a rather deep wallet where money us no issue and you enjoy the routine maintenance that comes along with large flooded battery banks. On the other hand, if all you use are a few lamps and a Dremel, and maybe a fan, then it is much more reasonable, but still quite expensive versus utility power where such is already available (the couple lights plus a Dremel solution will still set you back on the order of $1500-2500 depending upon how "hacked" together the setup is versus a more proper and reliable setup -- deep cycle batteries of several hundred Ah capacity, a few hundred watts of solar, a charge controller, and, finally, a 1000W true sine wave inverter plus wire and fittings). Literally doing a typical workshop with a typical assortment of portable and stationary loads and the sky becomes the limit depending upon your peak amp draw demands and how many KWh's of capacity you need -- start at $10K (for a rather small setup with just a few KWh of solar power and battery storage capacity and a couple KW of peak inverter capacity) and build up from there as needed. Remember that the peak amp draw of a large motor is typically 3-5 times its peak running amperage and your AC inverter must have sufficient headroom to handle that surge load and the batteries, and their wiring, must be sized large enough to ensure that the voltage drop does not become excessive during those surge events (if the voltage drop is too great under load then the inverter will go into low voltage shutdown even if you have an otherwise fully charged battery...everything has to be sized to work together as a well integrated system).
You must keep in mind that not only do you need sufficient solar panel capacity to capture your daily KWh usage each day within a roughly 6 hour "full sun equivalent" window (winter weighted), but you also need charge controllers, AC inverters (120V and/or 240V depending upon your shop equipment) with sufficient headroom to handle starting large induction motors, and a suitably large bank of true deep cycle traction batteries to store that charge so that demand can be met as needed. When sizing your battery bank you really have to overshoot capacity wise as the accessible amp-hour capacity of a battery decreases significantly the higher the peak amp draw will be, so you really need a handle on what your peak and average amp loads are going to be (at battery voltage, not AC voltage) coupled with how many KWh of energy storage (plus inverter losses of 10-15%) your shop will need to meet all your demands you will present over the typical lifespan of those batteries. The bottom 20% of any deep cycle lead acid battery is essentially off limits, so you have to oversize by a further 25% so they do not ever discharge deeper then 80% and also be aware that as the battery approaches end of life it will have lost another 20-30% of its capacity, so ideally you want to oversize again by a similar amount (which pays dividends, though, since your typical depth of discharge will then be far less with the oversized battery bank, improving battery cycle life).
Flooded lead acid batteries will fair best if charged using a 3 or 4 stage smart charge controller (which may, or may not, be built into your inverters) that carefully regulates their charging voltage levels and which performs periodic equalization charges to keep all the cells equalized as the batteries age. Such a charge controller will greatly improve battery life and tremendously reduces water and electrolyte losses reducing maintenance demands. Flooded lead acid batteries need to be regularly monitored at regular intervals (the exact interval is something you must learn as it will vary with your specific setup and use patterns) and the electrolyte levels in each and every cell checked for level and topped off, as needed, with distilled or deionized water to ensure that the top of the plates are never exposed to the air (which is both an internal explosion hazard and also severely damages the plates should such occur, so keep them topped off). If you have a very well regulated setup then the service interval may be every few months, but can be as often as every couple weeks if the batteries are getting abused by the charge controller (such as with a basic "dumb" constant voltage float charger, particularly if that float voltage is set a few tenths of a volt too high!).
I do not mean to scare you, but unless your needs are very small with very modest and predictable loads or you you are just hardcore interested in solar where money and time is not an issue, then trying to be totally off grid with solar is quite expensive as you must have oversized inverters plus maintain an expensive battery bank which must be replaced about every 4-6 years. While an ugly hacked together setup can be done on somewhat of a budget by comparison, I really advise against heavily hacked together setups as the amperages available from a suitably large battery bank are more than capable of setting a home or shop on fire if corners are cut and a well secured and safe install is not made (a standard that many heavily hacked systems tend to fall well short of if not built by a skilled electrician with everything properly and appropriately fused for the wire gauge used and all connections well secured and immobilized so that there is no chance of loose connections shorting).
When shopping for AC inverters you will want to limit yourself to the "true/pure" sine wave type and avoid the "modified" sine wave inverters (which are really just modified square wave inverters) as only the true sine wave inverters are appropriate for motors and other heavily inductive loads such as are found in a workshop. Also, when battery shopping, avoid "hybrid" trolling and marine deep cycle" batteries as they are not true deep cycle batteries and will fail prematurely when subjected to heavy cycling. Your best bang for the buck are 6V and 8V golf cart traction batteries (around 65 pounds each) followed by the T105/L16 size (around 115 pounds in either 2, 4, 6, or 8V configurations) traction batteries. Flooded lead acid batteries are the cheapest approach by far, but if money is not an issue then you might prefer sealed AGM batteries (at 3-5 times the cost for a given equivalent capacity) as they can not spill, require no maintenance, and do not emit explosive gasses under normal circumstances).
For some reference, I have an analogous non-solar implementation that maintains emergency power to my amateur radio gear during extended outages ensuring I can remain fully up and running for at least 12-24 hours at a time between 4 hour recharge intervals via generator. The present capacity is 230Ah at 12V (comprised of two 6V golf cart batteries in series), or 2.2KWh (12Vx230Ahx80%=2,200Wh) of effective storage capacity. It is kept charged via utility mains or generator (during an outage) and can be charged to greater than 90% state of charge in under 4 hours, or fully topped off in about 24 hours (if on mains power). Save for the lack of solar panels and a solar (instead of mains powered) charge controller this is effectively the same as a very tiny off-grid solar setup with 2.2KWh of useful storage capacity -- literally just plugin a true sine wave AC inverter and the solar panels and you are set. Even this modest setup with the pair of batteries, dual battery box, smart charge controller, fuses, circuit breaker, and heavy wiring represents nearly a $1000 investment in materials. On top of that, figure you would still need to add on the costs of a suitable AC inverter and about 400-500W of solar panels if you want to be able to fully charge that battery bank in a typical sunny fall/spring day. Scale up battery, inverter, and solar capacity, and the budget, as needed from there.
Good luck, whichever way you may opt to go!