Are you looking to play online, casually with friends, in a league, at local tournaments, or compete at higher levels? Depending what your goals and expectations are may change what a good recommendation is. Also, what's the estimated budget you're looking to spend? Is $20, 50 or 100 low to you to spend on a card game? Typically low means no Shaymins, which can limit your deck options so I'll mention the one tournament placing deck I know of without the little guy.
You mention you have the battle arena deck, which gives good water support like Dive Ball and Rough Seas, in addition to a few key cards like VS Seeker. Look into building Greninja Break. That deck does not need Shaymin. The most expensive card is the Break, which goes for about $12 last I checked. I play mine with two Breaks, but many people want three. That's going to total $36 if you want three. There are two common versions, Talonflame and Octillery, which both go for $3. Just call it another $10 as you'll want at least three Talonflame if you go with that version, or two Octillery if you go with that version, but you'll also need two Remoraids (Common card, .25 each).
The other pieces of the Greninja line are not expensive, should be less than $1 each.
Can you list out what Trainer cards you already have, at least the ones that would fit into this deck if you're interested in it? You'll want a full four count of Dive Ball .50 and VS Seeker $4 for sure, past that you have some flexibility in your counts of Sycamore and N, many players use Bursting Ballons and Wally also. Other things can be subbed in like you can use Shauna for N or Birch for Sycamore, not considered perfect substitutes, but can work when you're first starting out. Look at a full deck list in the garage section and find one that interests you.
Overall I think you could get the entire deck from singles for $75 or less if you started from nothing, which you are not since you already have some of the supporter cards. I didn't take the time to add up the cost of any lists so that's just a rough estimate.
Greninja Break is the only tournament placing deck I can think of that does not run Shaymin, looking at London results there was one that placed in the top 8. Other non-Shaymin decks include Riachu-Bats, Magnazone variants, and a few others, but they are not considered as competitive as Greninja Break.
Also, if you're just playing with friends or at a league, (Not a mutually exclusive scenario!) ask if you can use proxies. Put on a slip of paper what the "Fake" card is, sleeve it with a backwards card so you can shuffle, and play as if you had that card. It's a good way to see if you would like the deck before dropping money on it, but it's never allowed in formal tournaments, and even some leagues discourage it so check first.
(All my prices estimates came from TCGplayer.com as of this morning, they can and do vary as stock changes)
