Here’s what Rams should be shopping for in free agency

Negotiating deals for the annual NFL free-agent shopping spree begins Monday, with talks between teams and player agents allowed for 48 hours before contracts can begin to be signed Wednesday.

The Rams, perhaps the NFL’s savviest bargain hunters this offseason, did not wait for the doors to open. They spent the last few weeks making a dizzying series of headline-grabbing deals that remade their defense. So their shopping cart already is overflowing, with cornerbacks and salary-cap space to address other needs.

The Rams made trades to acquire Pro Bowl cornerbacks Marcus Peters and Aqib Talib. They signed veteran cornerback Sam Shields. They put the franchise tag on safety Lamarcus Joyner.

They thanked veteran linebackers Robert Quinn and Alec Ogletree for helping them make the playoffs for the first time since 2004 — and then unloaded their combined salary-cap number of more than $21 million to Miami and the New York Giants, respectively.

All of the trades, which become official Wednesday, netted draft picks and relieved pressure to overspend for a free-agent cornerback, or use their first-round pick to select one.

The Rams could have about $37 million in cap space and it could grow to $40 million if, as expected, the Rams release receiver Tavon Austin.

It is all part of the plan to build on last season’s 11-5 finish and NFC West title, while clearing room for a potential history-making extension for defensive tackle Aaron Donald this year, and running back Todd Gurley and quarterback Jared Goff down the line.

Last year the Rams invested heavily in free agents on offense, signing receiver Robert Woods, left tackle Andrew Whitworth and center John Sullivan, among others. The offense went from the worst in the NFL to one of the best.

The Rams have spent this offseason improving the defense. And there is more work to be done. Here are some areas the Rams might address through free agency:

Receivers

Wait a minute: Didn’t Woods show he was more than a possession receiver? Didn’t rookie Cooper Kupp burst onto the scene?

Yes, but the Rams’ primary free-agent target could be Sammy Watkins, who played for them last season after a training camp trade from the Buffalo Bills.

The Rams chose to put the franchise tag on Joyner at $11.2 million rather than on Watkins at nearly $16 million. But they still want Watkins if the price is right.

That price might have gone up last week when the Tampa Bay Buccaneers signed receiver Mike Evans to a five-year, $82.5-million extension that guarantees $55 million and averages $16.5 million per season.

Edge rushers

Quinn had 8½ sacks last season, but the Rams are searching for players who better fit coordinator Wade Phillips’ 3-4 scheme.

Adrian Clayborn of the Atlanta Falcons had a tackle for a loss in the Rams’ wild-card playoff defeat. Trent Murphy did not play for the Redskins last season because of a knee injury, but he has a Washington history with several members of the Rams’ staff, including coach Sean McVay and linebackers coach Joe Barry.

Junior Galette, who played for Washington last season, spent five seasons with New Orleans when Rams defensive line coach Bill Johnson was part of the Saints’ staff.

Rams linebacker Connor Barwin is a pending free agent, but he could return despite the emergence of rookie Samson Ebukam. The departures of Ogletree and Quinn leave a void in locker room leadership. Barwin could play an even larger role in 2018 in that regard.

Inside linebackers

The Rams ranked 28^th against the run last season, just sent Ogletree to the Giants, and must manage Mark Barron’s physical condition on a weekly basis.

Cory Littleton played well when called upon last season, but the Rams almost certainly will address this spot in free agency and the draft.

Avery Williamson, 26, who played well last season for the Tennessee Titans, is among the linebackers available in a pool that Phillips must evaluate to determine who best fits in his defense. Williamson had five tackles against the Rams last season.

NaVorro Bowman, a longtime San Francisco 49ers standout who played the second half of last season for the Oakland Raiders, also is among those available, but he’ll be 30 at the end of the month and is not a long-term solution.

The Rams also could be in the market for interior linemen to rotate in and augment the run defense.

Offensive linemen

Based on his outward physical condition, the 36-year-old Whitworth appears as if could play four more seasons. But the Rams know they must find an eventual replacement for him, as well as pending free-agent center Sullivan.

The Rams would like to re-sign Sullivan and find successors to both him and Whitworth through the draft, young players who can learn from the veterans.

Starting guards Rodger Saffold and Jamon Brown, and right tackle Rob Havenstein also are entering the final year of the their contracts.

Ryan Jensen of the Baltimore Ravens and Weston Richburg of the Giants are among pending free-agent centers. The Rams also could make a run at Giants center Brett Jones, a restricted free agent.

gary.klein@latimes.com

Follow Gary Klein on Twitter @latimesklein