Outdoor power supply for astrophotography

The usual choice is either an automotive lead acid battery (cheap, heavy, what I use) or a similar lithium battery (expensive, light).  Most stuff runs on 12VDC, there are inexpensive DC-DC converters for stuff that doesn't.  Example - for the laptop, something like this (if they run on the usual 19V).

https://www.amazon.com/uxcell-Converter-Regulator-Waterproof-Transformer/dp/B01H97ETP8/ref=cm_cr_arp_d_product_top?ie=UTF8

There are fancy options, which tend to cost a lot for their storage capacity.  100 Euro will not be enough.

Unfortunately, astrophotography tends not to be "plug and play', there's often some work involved.  The key thing to watch out for is getting the polarity right, astro equipment is often not protected against reverse polarity.

I use a deep cycle marine battery. It is rated at 110 aH. Buy from your local store as it will be drastically cheaper than ordering on Amazon. It cost me about $75 USD. But adapters/converters/chargers will run you another $40-50 USD.

Yes to the deep cycle marine battery.  Add a case, a trickle charger, and a 300W invertor for the laptop.  It will weight about 70lbs so you might include a small hand truck.  If you don't go too fancy, you should be within your budget.

Nico Carver:
As others have said, the best low-cost option for powering all that for a full night of imaging is a deep cycle lead acid battery. The one I got from Walmart lasted for five years of heavy use before I swapped it out for a new one (it was still working, but at only about 50% capacity). In addition to the battery itself, you will want a trickle charger to keep it maintained when not using. Other extras would be a battery box, and some way to hook up all the devices to the battery (many options).

+1 on what Nico said and I will add more detail from my experience.

I got a 12v to 19.5v converter with a plug that fits my Dell XPS13.  For my MYT I got a ~$30 12v to 48v converter.  All other equipment was already running on 12v so I no longer need an inverter.  This means no DC to AC to DC conversions to waste precious electrons.

I bought an Anderson powerpole kit that includes the crimper and cable to fashion the power cables.  I must stress this was way easier than I thought to make reliable cables of the correct length.

I am using a power+USB distribution box mounted on top of the scope.  Pegasus makes them but I am using a beta version of the one Feathertouch is coming out with.   It accepts a powerpole 12v input.   The Pegasus box uses a different input plug, but those are available for a few $ on Amazon.  So, from the battery(ies) there is one cable to the power unit, one to the laptop and one to the mount.

For my MYT, QHY600M, FLI FW, Ultrastar guider, Pegasus dew heater, and Dell XPS13, about 100 amp hours is needed to safely get through the night.  Since lead acid deep cycle batteries can't full draw down their charge, two 75 amp hour batteries do the trick.  The two can be hooked up together with a couple of cables or you may run the powerbox on one and the mount+laptop on the other.

This is about the amount of power I can get recharged using my 100 watt solar panel on a sunny Summer day.

Including the cost of the powerbox, batteries, powerpole kit, various cheap cables I cut up, and the two converters from Amazon, this is under $1000.   Any maybe even including the solar panel.  Didn't check current prices but that about what I remember.

Avoid inverters, some of them do not work properly in humid conditions. As most of the astronomy equipment is designed for 12V, a 12V lead acid, placed under the tripod is a good start.
You can use "generic" Lead Acid batteries from companies like CSB, which easily can go to 40Ah and more.
First as people said before, measure your equipment, how much power you need. This way you can calculate both the size of the battery AND the size of a fuse (use automotive type fuses) to put as close to the battery as possible. Large batteries can easily start fires when shorted.
For the notebook, use a DC-DC converter (search for Automotive adapter) which will easily, with low loss, convert 12V to 18.5/19/19.5V whatever your notebook uses. It is also wise to start the evening with the notebook battery fully charged. This way you will not spend your main battery's juice to charge the notebook. And also, if at the end of the evening the battery starts to get a little bit low, unplug the notebook and let it run on its own battery.
Mounts do not consume a lot of power unless slewing. So when they track their power use is minimal.
You do not have an astro camera, where its peltier elements will consume a lot of power - this is good.
In the night the screen of the notebook will be at minimum brightness, also good.
As a rough estimate: 1.5A mount, 1A dew heater, 40W notebook=3.5A, guide camera will be powered from notebook, Canon 0.1A or less so in total 1.5+1+3.5+0.1=6.1A . 6 hours imaging = 37Ah.
So something like CSB GP 12400 (40Ah) will do the job. Less than 100 euro. And the numbers are conservative, the notebook will not constantly draw 40W if it is a fairly new one, the mount will draw less under tracking and within the last two hours you can unplug your notebook to save juice.
DO NOT FORGET THE FUSE! Put something like 10A fuse close to the positive lead of the battery, any car electrician can help you on this.

If you don´t have ten thumbs and 2 left hands and you understand anything from electric, build your own powertank with what you need. Cheap base is a car battery and a DC-DC-converter (if your notebook needs 19V). My tank had cost ca. 220€ but with some features and is big enough to power mount, notebook, cooled cameras, focuser, filter wheel etc. for over 12 hours.

https://www.astrobin.com/7hc16n/