So a budget R/G landfall that might win a few games here or there... this is doable:
4x Monastery Swiftspear - it's a hasty 1-drop that is almost never a 1/2 and can sneak in tons of damage without too much trouble.
4x Scythe Leopard - your other 1-drop that needs little explanation. Seldom a 1/1, more likely a 2/2 or larger.
4x Snapping Gnarlid - same story as leopard, slightly larger edition.
4x Makindi Sliderunner - similar to the gnarlid, but more importantly with trample - gotta force that damage through.
2x Valakut Predator - this isn't a traditional choice, but from a budget angle, it's the only 3-drop you run, it quickly and easily becomes a 4/4, and will help get the job done. Odds are you don't want a full 4x, as it benefits you to keep the curve low, but it's enough to help.
This creature base really isn't that different from the R/G lists that just did quite well at the pro-tour. The idea is to drop a few creatures, keep triggering landfall, and use pump spells to finish the job.
Now the pumps:
2x Become Immense - stuff WILL hit the yard and the appeal here is to provide something sizable do do with all the cards in there.
4x Swell of Growth - here's your budget Atarka's Command. It helps pump one while allowing for a second landfall trigger to pump the whole team.
4x Temur Battle Rage - this is the bee's knees of pump spells. You can use it to force the last bit of damage through or for a really explosive hit. Note that you should almost never use this on anything that has less than 4 power, as you want the trample effect just as much as the double-strike.
4x Titan's Strength - pumps, scry, generally your all around-combat trick. This can turn into a MAJOR beating if you use it on the sliderunner, swiftspear, or anything unblocked (especially with battle rage backup).
2x Retreat to Valakut - it pumps, it makes blocks difficult, it generally just makes landfall that much better. Normally this would be the definition of a win-more card (one that's only good when you're already winning), but the ability to pump for battle rage r to push that last bit of damage through by stopping the opponent from blocking is actually the real deal.
1x Outpost Siege - here's the top of your curve. Odds are you're not going to need this, but you can select Khans mode to "draw" an extra card per turn. Just remember to play things exiled before stuff you draw, as the exiled stuff goes away.
1x Crater's Claws - you're going to be hitting landfall EVERY turn. Eventually, pending the game goes past turn 4-6, you will want something to sink all your mana into. This can be a surprise finisher if you stall out with the opponent at 5-6.
Please double-check my math, but that SHOULD work out to 36 cards. The remaining 24 should be lands. Now the idea to use fetch lands is to provide 2x landfall triggers per turn while still providing untapped sources to then use to cast the various pumps. Sadly, this is the expensive part of the deck, where, for a budget option, you're sort of in a lurch. But, all is not lost, as there are somewhat "workable" fetch options at your disposal. I would propose the following manabase:
3x Forest
11x Mountain
4x Rugged Highlands
These are self-explanatory. You want to ensure that you have some green at your disposal, but as the majority of the deck operates on red, you want to be sure you have access to much more red than green at any given point.
4x Evolving Wilds - here's the "poor man's fetchland." You can use this to ensure you get any green you might need. But, more importantly, it provides you 2x landfall triggers in one turn OR a single landfall trigger when it enters and another one at instant speed whenever you really need it.
2x Blighted Woodland - I've yet to really figure out the optimal use of this one myself, but it can provide as many as 3x landfall triggers in one turn OR 2x landfall triggers at instant speed.
This SHOULD be a workable 60 that will score a few wins here or there (perhaps even 1-2 rounds at gameday). I'd suggest trying the deck out to the extent that you can, even if it's just goldfishing (playing solo) to familiarize yourself with the ins-and-outs of the deck, timing for the wilds and woodlands, sequencing of lands and plays, etc.
As for a sideboard, honestly, with a limited card pool to draw on and budget to work with, I wouldn't even really bother with it too much. If you want to have a few copies of Wild Slash to deal with other aggro builds, 2-3 Grove Rumblers in the event you need to go more mid-range, 2-3 Magmatic Chasm if the opponent has ways to flood the board and bog the game down, and some copies of Naturalize, Roast, and Goblin Heelcutter for other scenarios. The dash ability of heelcutter will help combat control decks.
Let me know if you have any questions. I hope this helps.
Good luck!