The Senate is facing fights over arms control and NATO this week as it considers both a Pentagon budget bill and the historic U.S.-Soviet treaty eliminating medium-range nuclear weapons.

First, the Senate will begin work on the military budget, an annual fight that generally involves wide-ranging decisions on America's far-flung commitments.The bill approved by the Senate Armed Services Committee authorizes $299.5 billion for the Pentagon and targets increased spending for non-nuclear weapons in the North Atlantic Treaty Organization.

"This issue of conventional weapons in NATO is something that we paid an awful lot of attention to this year, given the treaty," said Sen. Sam Nunn, D-Ga., chairman of the panel.

He was referring to the Intermediate-range Nuclear Forces treaty signed Dec. 8 by President Reagan and Soviet leader Mikhail S. Gorbachev.

It eliminates both nations' medium-range missiles, and Nunn and other supporters say NATO's non-nuclear defenses will have to be bolstered after the missiles are gone.

The Senate is tentatively scheduled to begin work on the treaty Wednesday.

During the Pentagon bill debate, amendments are likely to increase spending for NATO and urge U.S. allies in the 16-nation alliance to pay more of NATO's costs.

Also expected are proposals providing advice to Reagan from both conservative Republicans and liberal Democrats about the arms control policies he should follow in the last six months of his administration.

Similar attempts were made the past two weeks in the House during that chamber's work on its version of the Pentagon budget bill. The House approved nuclear arms control restrictions opposed by the administration, along with cuts in "Star Wars" missile defense spending that were so deep that Defense Secretary Frank Carlucci threatened to advise Reagan to veto the bill.

The House is expected to give final approval Wednesday to its Pentagon bill. Similar action by the Senate will send the separate measures to a House-Senate conference committee to reconcile the differences.

Both measures propose $299.5 billion for the Pentagon in the fiscal year starting Oct. 1.