Would love to get into the world of mountaineering

You don't need high mountains to learn the basic skills, on the contrary. You learn rock climbing first, you can learn anything on a 10m high wall and even on boulders. Than do a winter course in high Alpine mountains where you learn how to move on snow and ice, avoid avalanches, etc.

Join the nearest branch of the Israel Climbers Club.

Once you learned the basics I'm sure you can join trips to higher mountains(Alps, Caucasus, etc) and find climbing partners.

Did you already finished your military service? If not, you could try to apply to serve in a unit where they teach you climbing(Golani?, etc.)

yeah im done with the army 5 years ago. nice knowledge though :)
and thanks of course, any idea on how much money do i need? its not a cheap hobby

Until you get to the level to climb 6-8000m high peaks with expensive climbing permits it's just as expensive as travelling. Your main expense will be the plane ticket from Israel to wherever. Than it's mostly camping and cooking for yourself, unless you go to areas with mountain huts, like the Alps, but even than 2 weeks in the mountains is always cheaper than 2 weeks sightseeing from city to city.

As for the equipment you spend as much money on it as you can afford. Read a liitle bit about world famous Polish climber Jerzy Kukuczka. He was climbing in the 80's when everything was in short supply in Poland(including money), he didn't have any fancy gear, yet still managed to climb almost every 8000m peak.

If you don't do any technical climbing you don't need that much gear anyway. The only piece of gear where you should not think about saving money or buying used stuff is the rope, he, he. :-)

Until you get to the level to climb 6-8000m high peaks with expensive climbing permits it's just as expensive as travelling. Your main expense will be the plane ticket from Israel to wherever. Than it's mostly camping and cooking for yourself, unless you go to areas with mountain huts, like the Alps, but even than 2 weeks in the mountains is always cheaper than 2 weeks sightseeing from city to city.

As for the equipment you spend as much money on it as you can afford. Read a liitle bit about world famous Polish climber Jerzy Kukuczka. He was climbing in the 80's when everything was in short supply in Poland(including money), he didn't have any fancy gear, yet still managed to climb almost every 8000m peak.

If you don't do any technical climbing you don't need that much gear anyway. The only piece of gear where you should not think about saving money or buying used stuff is the rope, he, he. :-)

thank you for your time and this answer :)

Dig out the memoirs of late Jerzy Kukuczka. He managed to climb all 8000m peaks and almost beat the richly sponsored Reinhodt Messner to be the first one, practically without money. On one 2 month expedition to Pakistan they could budget one bottle of Coke for each climber during the entire trip, and the food they ate was worse than what the porters had. Still he climbed all the peaks either by a new difficult route or as a first winter ascent.

Kukuczka was brilliant and his sheer natural talent/ability probably made up for a lot of his sub-standard gear. But others were not nearly so lucky. Good gear is really key these days, whether you buy it new or from reliable second hand sources. Most of us don't have that pure natural talent or drive. There are plenty of other stories of climbers dying, at least in part due to poor gear.

From my experience, to start mountaineering, you start with the snow/scrambling/glacier skills, and add on the technical rock skills. Running is great, but you need to work on hills/scrambling/squats to build core/leg strength. Though if you've been through the army, you are probably in really great shape! Find an indoor climbing gym - learn how to belay, rappel (if you haven't already), handle rope and basic climbing movement. And eventually to lead. But don't worry about advanced climbing - gym climbing is not really like outdoor climbing and you don't need to be able to do much more than a solid 5.7 to do most alpine routes.

Then find a good mountaineering course - in Europe or Asia, which will teach you how to travel on a glacier, walk on crampons, do crevasse rescue, rope up, navigate with a compass/map, make risk/likelihood/consequence decisions and work as a team. A good one will be given by guide(s) certified by an IFMGA member association, and last 4-7 days minimum. It's not an insignificant cost, but getting good basic instruction can make a big difference in learning the core skills and being able assess future trips/trip partners. And join local climbing/mountaineering associations - they can be a good source of low cost courses and low cost group trips.

As to gear/mountaineering - it's not cheap - and not always going to be as cheap as regular traveling. Though it depends on what you are doing, and what you are willing to sacrifice. Rope is important, but it's one part of the safety system - I wouldn't compromise on a harness, carabiners or ice tools/mountaineering axe. I would never buy a harness or biners second hand, other than in new/nearly new condition from a known source. All it takes is one drop on a hard surface to significantly reduce the safety of a biner. Camping is great, but you have to factor in camping/hut fees, access fees on some mountains, guides (where needed), gear (you are always replacing something!) and food. Plus medical insurance of some kind if you want to get medical treatment, and often a membership in some climbing association (which may include some insurance/rescue cover).

The basics will include mountaineering boots (type depending on the seasons you climb), harness, helmet, belay device, a few biners, a good pack and a mountaineering axe. Plus decent clothes - you can slowly build up a wardrobe via sales and discounts, but while the quality brands may be expensive, they are worth the money. There are some good inexpensive brands, but for the most part, it's the more expensive brands that are the best quality, last the longest and offer the best return/exchange/warranty policies. Then you can add on more climbing gear as needed (i.e. slings, rope, cordelette, quick draws, carabiners, quicklinks, prusiks, ice tools) depending on where and what you are climbing. If you get into winter stuff, then that may be more expensive - i.e. backcountry skis, poles, boots, helmet etc.

Many Israelis go to the mountains of Georgia for their holidays, I gues these are the closest high mountains to Israel, very worthwhile.