I don't mean to sound dismissive but it sounds, from the phrasing if the question, like you don't have much knowledge or experience at long range. No worries, enthusiasm is what we all start with.
Everyone has offered many great tips and suggestions for your max range but I would suggest a different approach. I would suggest you focus your introduction to "learning long range on a budget" to mastering up to 1000yrds. You will do much better, eventually, at 2000 yards if you have more trigger time reading wind, learning proper fundamentals at medium to long ranges. A .223 will teach you that 600 can be a challenge. A 6.5creedmoor is probably your best off the shelf option for cheap/good ammunition to get good trigger time and reach out to reasonable distances. You will learn there is a large difference between 600 and 800 yards and an even bigger difference between 800 and 1000 and so on. Get a .308 if you budget is minuscule as barrel life will be 2-3x tgat of the 6.5 Creedmoor and the "disadvantages" of the .308 will teach you to master the wind calling needed for ELR shooting later.
When you jump from Long Range to ELR you will need to step up in the equipment department as well as refine your ballistic data, get into precision reloading and afford less trigger pulls.
For example: A range finder for Long Range can be had in the $200-400 like a Sig Kilo 2200 but this is not suitable for ELR